Could you not just have the value as a computed column, then there is no need to update, as it's calculated? For example:
USE DevTestDB;
GO

CREATE TABLE Dates (ID INT IDENTITY(1,1),
                    Start_Date DATETIME,
                    End_Date DATETIME,
                    DIFF AS (DATEDIFF(MINUTE,Start_date,End_Date)));
GO

INSERT INTO Dates (Start_Date, End_Date)
VALUES ('15-Jan-2016 19:19:19.000', '15-Jan-2016 20:20:20.000'),
       ('16-Jan-2016 10:10:00.000', '16-Jan-2016 16:45:22.000');
GO

SELECT *
FROM Dates;

UPDATE Dates
SET End_Date = '16-Jan-2016 12:17:22.000'
WHERE ID = 2;

SELECT *
FROM Dates;

GO
DROP TABLE Dates

This brings back the following respectively:
ID          Start_Date              End_Date                DIFF
----------- ----------------------- ----------------------- -----------
1           2016-01-15 19:19:19.000 2016-01-15 20:20:20.000 61
2           2016-01-16 10:10:00.000 2016-01-16 16:45:22.000 395

(2 row(s) affected)

ID          Start_Date              End_Date                DIFF
----------- ----------------------- ----------------------- -----------
1           2016-01-15 19:19:19.000 2016-01-15 20:20:20.000 61
2           2016-01-16 10:10:00.000 2016-01-16 12:17:22.000 127

(2 row(s) affected)