How about...

USE Sandbox;
GO
/*
All odd alignment issues courtesy of SSC's text editor :)
*/

CREATE TABLE SampleTable (ID int IDENTITY(1,1),
         StartDay varchar(9),
         EndDay varchar(9));

INSERT INTO SampleTable
VALUES ('Monday','Friday'),
   ('Tuesday','Wednesday'),
   ('Friday','Monday');
GO

CREATE FUNCTION DayNumber_fn (@DayName varchar(9))
RETURNS TABLE
AS RETURN

  SELECT CASE @DayName WHEN 'Sunday' THEN 0
         WHEN 'Monday' THEN 1
         WHEN 'Tuesday' THEN 2
         WHEN 'Wednesday' THEN 3
         WHEN 'Thursday' THEN 4
         WHEN 'Friday' THEN 5
         WHEN 'Saturday' THEN 6 END AS DayNum;

GO

SELECT ID,
   (7 + (ED.DayNum - SD.DayNum) ) % 7 AS [Days]
FROM SampleTable ST
  CROSS APPLY dbo.DayNumber_fn(ST.StartDay) SD
  CROSS APPLY dbo.DayNumber_fn(ST.EndDay) ED;

GO
DROP TABLE SampleTable;
DROP FUNCTION DayNumber_fn;

I've used a Inline table Function here, however, you could move the CASE into the main query and use a CTE. A The use of the function just makes the final query a little more little more succinct.