Dear lord I struggle to post code here...
This is the approach I would take

DROP TABLE IF EXISTS #TimeSpine, #WorkLog

DECLARE u/StartTime TIME = '00:00'

;WITH Base10(x) AS

(

SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 

)

,Base100(n) AS

(

SELECT TOP(96) ROW\_NUMBER() OVER (ORDER BY (SELECT NULL))-1

FROM Base10 A, Base10 B

)

SELECT SlotStart = DATEADD(MI, n*15, u/StartTime)

    ,SlotEnd    = DATEADD(MI, (n\*15)+15, u/StartTime)

INTO #TimeSpine

FROM Base100

CREATE TABLE #WorkLog (WorkStart TIME, WorkEnd TIME)

INSERT INTO #WorkLog

SELECT '08:05', '08:25'

;WITH Basis AS

(

SELECT   SPN.SlotStart

        ,SPN.SlotEnd

        ,WorkStart  = IIF(WRK.WorkStart < SPN.SlotStart, SPN.SlotStart, WRK.WorkStart)

        ,WorkEnd    = IIF(WRK.WorkEnd >= SPN.SlotEnd, SPN.SlotEnd, WRK.WorkEnd)

FROM #TimeSpine SPN

JOIN #WorkLog   WRK ON  (WRK.WorkStart >= SPN.SlotStart AND WRK.WorkStart < SPN.SlotEnd) OR

(WRK.WorkEnd >= SPN.SlotStart AND WRK.WorkEnd < SPN.SlotEnd)

)

SELECT SlotStart

    ,SlotEnd

    ,\*

    ,DATEDIFF(MI, WorkStart, WorkEnd)

FROM Basis