Query

This uses a pivot table...


USE [tempdb];

CREATE TABLE dbo.Requested
(Pkey Int, ParentId Int, [Status] Varchar(50), Datelogged DateTime);

SET DATEFORMAT DMY; -- To get British dates

INSERT INTO dbo.Requested
VALUES
(1,    123,    'Submitted',    '12/9/2018 10:30'),
(2,    123,    'Assigned',    '12/9/2018 10:40'),
(3,    123,    'Acknowledge',    '12/9/2018 10:45'),
(4,    123,    'OnHold',    '12/9/2018 10:55'),
(5,    123,    'Resolved',    '12/9/2018 11:15'),
(6,    124,    'Submitted',    '12/9/2018 10:30'),
(7,    124,    'Assigned',    '12/9/2018 10:40'),
(8,    124,    'Acknowledge',    '12/9/2018 10:45'),
(9,    124,    'OnHold',    '12/9/2018 10:55'),
(10,    124,    'Work In Progress',    '12/9/2018 11:16'),
(11,    124,    'Resolved',    '12/9/2018 11:45');

WITH CTE AS
(
SELECT ParentId, 
[Submitted], [Assigned], [Acknowledge], [OnHold], [Work In Progress], [Resolved]
FROM
(SELECT ParentId, [Status], Datelogged 
  FROM dbo.Requested) AS SourceTable
PIVOT
(
MAX(Datelogged)
FOR [Status] IN ([Submitted], [Assigned], [Acknowledge], [OnHold], [Work In Progress], [Resolved])
) AS PivotTable
)
SELECT ParentId, 
    [Submitted], [Assigned], [Acknowledge], [OnHold], [Work In Progress], [Resolved],
    [TotalResolvedTime] = DATEDIFF(mi,[Submitted], [Resolved]),
    [ActualResolvedTime] = DATEDIFF(mi,[Submitted], [Resolved]) - CASE WHEN [Work In Progress] IS NULL THEN DATEDIFF(mi,[OnHold], [Resolved]) ELSE DATEDIFF(mi,[OnHold], [Work In Progress]) END
FROM CTE;


You can use LEAD to get the time between OnHold and the next status

CREATE TABLE #temp
(
[Pkey] INT,
[ParentId] INT,
[Status] VARCHAR(40),
[Datelogged] DATETIME
)

INSERT INTO #temp
VALUES
(1,123,'Submitted','12/9/2018 10:30'),
(2,123,'Assigned','12/9/2018 10:40'),
(3,123,'Acknowledge','12/9/2018 10:45'),
(4,123,'OnHold','12/9/2018 10:55'),
(5,123,'Resolved','12/9/2018 11:15'),
(6,124,'Submitted','12/9/2018 10:30'),
(7,124,'Assigned','12/9/2018 10:40'),
(8,124,'Acknowledge','12/9/2018 10:45'),
(9,124,'OnHold','12/9/2018 10:55'),
(10,124,'WorkInProgress','12/9/2018 11:16'),
(11,124,'Resolved','12/9/2018 11:45');

WITH TimeInStateCTE AS
(
  SELECT
   [ParentId],
   [Status],
   DATEDIFF(MINUTE, [Datelogged],LEAD([Datelogged],1) OVER (PARTITION BY [ParentId] ORDER BY [Datelogged])) AS [timeInState]
  FROM #temp
),Final AS
(
  SELECT
   #temp.[ParentId],
   DATEDIFF(MINUTE, MIN(Datelogged),MAX(Datelogged)) AS [Total Resolved time (min)],
   DATEDIFF(MINUTE, MIN(Datelogged),MAX(Datelogged)) - tis.timeInState AS [Actual Resolved time (min)]
  FROM #temp
  CROSS APPLY (SELECT [ParentId], [timeInState] FROM TimeInStateCTE WHERE [Status] = 'OnHold') tis
   WHERE #temp.[ParentId] = tis.[ParentId]
  GROUP BY #temp.[ParentId], tis.timeInState
)
SELECT * FROM Final

DROP TABLE #temp

Try this on for size and performance:
CREATE TABLE #Requested (
    Pkey Int,
    ParentId Int,
    [Status] Varchar(50),
    Datelogged DateTime
);
INSERT INTO #Requested
    (
    Pkey,
    ParentId,
    [Status],
    Datelogged
    )
    VALUES    (1,  123,  'Submitted',  '12/9/2018 10:30'),
            (2,  123,  'Assigned',  '12/9/2018 10:40'),
            (3,  123,  'Acknowledge',  '12/9/2018 10:45'),
            (4,  123,  'OnHold',  '12/9/2018 10:55'),
            (5,  123,  'Resolved',  '12/9/2018 11:15'),
            (6,  124,  'Submitted',  '12/9/2018 10:30'),
            (7,  124,  'Assigned',  '12/9/2018 10:40'),
            (8,  124,  'Acknowledge',  '12/9/2018 10:45'),
            (9,  124,  'OnHold',  '12/9/2018 10:55'),
            (10, 124,  'Work In Progress',  '12/9/2018 11:16'),
            (11, 124,  'Resolved',  '12/9/2018 11:45');

WITH ELIGIBLE_CASES AS (

    SELECT R.*,
        CASE
            WHEN R.[Status] = 'Submitted' THEN R.Datelogged
            ELSE NULL
        END AS Submitted,
        CASE
            WHEN R.[Status] = 'Resolved' THEN R.Datelogged
            ELSE NULL
        END AS ResolvedDateLogged,
        DATEDIFF(minute, H.OnHoldDateLogged, LEAD(R.DateLogged, 1) OVER(PARTITION BY R.ParentId ORDER BY R.Datelogged)) AS OnHoldTime
    FROM #Requested AS R
    OUTER APPLY (
        SELECT
            CASE
                WHEN R.[Status] = 'OnHold' THEN R.Datelogged
                ELSE NULL
            END AS OnHoldDateLogged
        ) AS H
    WHERE EXISTS (
        SELECT 1
        FROM #Requested AS R2
        WHERE    R2.ParentId = R.ParentId
            AND R2.[Status] = 'Resolved'
        )
)
SELECT
    EC.ParentId,
    DATEDIFF(minute, MAX(EC.Submitted), MAX(EC.ResolvedDateLogged)) AS TotalResolutionTime,
    DATEDIFF(minute, MAX(EC.Submitted), MAX(EC.ResolvedDateLogged)) -
        SUM(EC.OnHoldTime)                                            AS ActualResolutionTime
FROM ELIGIBLE_CASES AS EC
GROUP BY EC.ParentId
ORDER BY EC.ParentId;

DROP TABLE #Requested;

Revising my previous version
CREATE TABLE #temp
(
[Pkey] INT,
[ParentId] INT,
[Status] VARCHAR(40),
[Datelogged] DATETIME
)

INSERT INTO #temp
VALUES
(1,123,'Submitted','12/9/2018 10:30'),
(2,123,'Assigned','12/9/2018 10:40'),
(3,123,'Acknowledge','12/9/2018 10:45'),
(4,123,'OnHold','12/9/2018 10:55'),
(5,123,'Resolved','12/9/2018 11:15'),
(6,124,'Submitted','12/9/2018 10:30'),
(7,124,'Assigned','12/9/2018 10:40'),
(8,124,'Acknowledge','12/9/2018 10:45'),
(9,124,'OnHold','12/9/2018 10:55'),
(10,124,'WorkInProgress','12/9/2018 11:16'),
(11,124,'Resolved','12/9/2018 11:45');

WITH Final AS
(
  SELECT
   [ParentId],
   [Status],
   DATEDIFF(MINUTE, [Datelogged],LEAD([Datelogged],1) OVER (PARTITION BY [ParentId] ORDER BY [Datelogged])) AS [timeInState]
FROM #temp
)
SELECT
  [ParentId],
  SUM([timeInState]) AS [Total Resolved time (min)],
  SUM(CASE WHEN [status] ='onHold' THEN 0 ELSE [timeInState] end) AS [Actual Resolved time (min)]
FROM Final
GROUP BY [ParentId]

DROP TABLE #temp...