There are a lot of interesting solutions to this problem (stated in different terms) here and its preceding pages. There it is presented as matching supply and demand in an auction. The units supplied/demanded is directly analogous to the days in an interval from this question so the solution translates. I've left it in the terms used in the linked site, though.

Sample data.

DROP TABLE IF EXISTS dbo.Auctions;
 
CREATE TABLE dbo.Auctions
(
  ID INT NOT NULL IDENTITY(1, 1)
    CONSTRAINT pk_Auctions PRIMARY KEY CLUSTERED,
  Code CHAR(1) NOT NULL
    CONSTRAINT ck_Auctions_Code CHECK (Code = 'D' OR Code = 'S'),
  Quantity DECIMAL(19, 6) NOT NULL
    CONSTRAINT ck_Auctions_Quantity CHECK (Quantity > 0)
);
 
SET NOCOUNT ON;
 
DELETE FROM dbo.Auctions;
 
SET IDENTITY_INSERT dbo.Auctions ON;
 
INSERT INTO dbo.Auctions(ID, Code, Quantity) VALUES
  (1, 'D', 5.0),
  (2, 'D', 3.0),
  (3, 'D', 8.0),
  (5, 'D', 2.0),
  (6, 'D', 8.0),
  (7, 'D', 4.0),
  (8, 'D', 2.0),
  (1000, 'S', 8.0),
  (2000, 'S', 6.0),
  (3000, 'S', 2.0),
  (4000, 'S', 2.0),
  (5000, 'S', 4.0),
  (6000, 'S', 3.0),
  (7000, 'S', 2.0);

The solutions expounded reduce the elapsed time for his 400k row sample data from a naive 11 seconds to 0.4s. The fastest is by Paul White (of this parish), shown here.

DROP TABLE IF EXISTS #MyPairings;
 
CREATE TABLE #MyPairings
(
  DemandID integer NOT NULL,
  SupplyID integer NOT NULL,
  TradeQuantity decimal(19, 6) NOT NULL
);
GO
 
INSERT #MyPairings 
    WITH (TABLOCK)
(
    DemandID,
    SupplyID,
    TradeQuantity
)
SELECT 
    Q3.DemandID,
    Q3.SupplyID,
    Q3.TradeQuantity
FROM 
(
    SELECT
        Q2.DemandID,
        Q2.SupplyID,
        TradeQuantity =
            -- Interval overlap
            CASE
                WHEN Q2.Code = 'S' THEN
                    CASE
                        WHEN Q2.CumDemand >= Q2.IntEnd THEN Q2.IntLength
                        WHEN Q2.CumDemand > Q2.IntStart THEN Q2.CumDemand - Q2.IntStart
                        ELSE 0.0
                    END
                WHEN Q2.Code = 'D' THEN
                    CASE
                        WHEN Q2.CumSupply >= Q2.IntEnd THEN Q2.IntLength
                        WHEN Q2.CumSupply > Q2.IntStart THEN Q2.CumSupply - Q2.IntStart
                        ELSE 0.0
                    END
            END
    FROM
    (
        SELECT 
            Q1.Code, 
            Q1.IntStart, 
            Q1.IntEnd, 
            Q1.IntLength, 
            DemandID = MAX(IIF(Q1.Code = 'D', Q1.ID, 0)) OVER (
                    ORDER BY Q1.IntStart, Q1.ID 
                    ROWS UNBOUNDED PRECEDING),
            SupplyID = MAX(IIF(Q1.Code = 'S', Q1.ID, 0)) OVER (
                    ORDER BY Q1.IntStart, Q1.ID 
                    ROWS UNBOUNDED PRECEDING),
            CumSupply = SUM(IIF(Q1.Code = 'S', Q1.IntLength, 0)) OVER (
                    ORDER BY Q1.IntStart, Q1.ID 
                    ROWS UNBOUNDED PRECEDING),
            CumDemand = SUM(IIF(Q1.Code = 'D', Q1.IntLength, 0)) OVER (
                    ORDER BY Q1.IntStart, Q1.ID 
                    ROWS UNBOUNDED PRECEDING)
        FROM 
        (
            -- Demand intervals
            SELECT 
                A.ID, 
                A.Code, 
                IntStart = SUM(A.Quantity) OVER (
                    ORDER BY A.ID 
                    ROWS UNBOUNDED PRECEDING) - A.Quantity,
                IntEnd = SUM(A.Quantity) OVER (
                    ORDER BY A.ID 
                    ROWS UNBOUNDED PRECEDING),
                IntLength = A.Quantity
            FROM dbo.Auctions AS A
            WHERE 
                A.Code = 'D'
 
            UNION ALL 
 
            -- Supply intervals
            SELECT 
                A.ID, 
                A.Code, 
                IntStart = SUM(A.Quantity) OVER (
                    ORDER BY A.ID 
                    ROWS UNBOUNDED PRECEDING) - A.Quantity,
                IntEnd = SUM(A.Quantity) OVER (
                    ORDER BY A.ID 
                    ROWS UNBOUNDED PRECEDING),
                IntLength = A.Quantity
            FROM dbo.Auctions AS A
            WHERE 
                A.Code = 'S'
        ) AS Q1
    ) AS Q2
) AS Q3
WHERE
    Q3.TradeQuantity > 0;