SQL Server 2012

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CREATE TABLE #Temp
(
  RoomTypeId INT,
  BedId INT,
  StartDate DATE,
  EndDate DATE
)

INSERT INTO #Temp
(RoomTypeId, BedId, StartDate, EndDate)
VALUES 
(39, 229, '2019-08-03', '2019-08-04'),
(39, 229, '2019-08-05', '2019-08-08'),
(40, 231, '2019-08-05', '2019-08-08'),
(41, 238, '2019-08-02', '2019-08-03'),
(42, 233, '2019-08-02', '2019-08-03'),
(42, 233, '2019-08-04', '2019-08-05'),
(42, 234, '2019-08-05', '2019-08-05'),
(43, 241, '2019-08-01', '2019-08-01'),
(43, 241, '2019-08-15', '2019-08-16'),
(43, 241, '2019-08-29', '2019-08-30'),
(45, 245, '2019-08-03', '2019-08-06'),
(45, 244, '2019-08-05', '2019-08-05'),
(45, 244, '2019-08-08', '2019-08-10'),
(45, 244, '2019-08-17', '2019-08-19'),
(46, 239, '2019-08-03', '2019-08-04'),
(46, 239, '2019-08-05', '2019-08-05'),
(48, 250, '2019-08-16', '2019-08-18'),
(49, 274, '2019-08-06', '2019-08-11'),
(49, 275, '2019-08-08', '2019-08-10')

SELECT 
        p.RoomTypeId,
        p.EndDateSeq1,
        p.StartDateSeq2,
        SUM(p.GAP) AS [GAP]
    FROM (
        SELECT 
            t.RoomTypeId,
            t.EndDate AS [EndDateSeq1],
            t2.StartDate AS [StartDateSeq2],
            DATEDIFF(d, t.EndDate,t2.StartDate) AS [GAP],
    		ROW_Number() OVER(PARTITION BY  t.RoomTypeId,t.StartDate ORDER By t2.StartDate) RN
        FROM #Temp t
        LEFT JOIN #Temp t2 ON t2.RoomTypeId = t.RoomTypeId 
            AND (t2.StartDate > t.EndDate) 
    ) p
    WHERE RN = 1
    GROUP BY p.RoomTypeId, p.EndDateSeq1, p.StartDateSeq2
    ORDER BY p.RoomTypeId, p.EndDateSeq1 ASC

RoomTypeId	EndDateSeq1	StartDateSeq2	GAP
39	04/08/2019 00:00:00	05/08/2019 00:00:00	1
39	08/08/2019 00:00:00	null	null
40	08/08/2019 00:00:00	null	null
41	03/08/2019 00:00:00	null	null
42	03/08/2019 00:00:00	04/08/2019 00:00:00	1
42	05/08/2019 00:00:00	null	null
43	01/08/2019 00:00:00	15/08/2019 00:00:00	14
43	16/08/2019 00:00:00	29/08/2019 00:00:00	13
43	30/08/2019 00:00:00	null	null
45	05/08/2019 00:00:00	08/08/2019 00:00:00	3
45	06/08/2019 00:00:00	08/08/2019 00:00:00	2
45	10/08/2019 00:00:00	17/08/2019 00:00:00	7
45	19/08/2019 00:00:00	null	null
46	04/08/2019 00:00:00	05/08/2019 00:00:00	1
46	05/08/2019 00:00:00	null	null
48	18/08/2019 00:00:00	null	null
49	10/08/2019 00:00:00	null	null
49	11/08/2019 00:00:00	null	null

Warning: Null value is eliminated by an aggregate or other SET operation.