Hopefully a little easier to read than Martin's. I used different tables and sample data, hopefully extrapolating the right info:
CREATE TABLE [dbo].[Quantity](
[PeriodStart] [date] NOT NULL,
[PeriodEnd] [date] NOT NULL,
[Quantity] [int] NOT NULL
) ON [PRIMARY]
CREATE TABLE [dbo].[SoldItems](
[PeriodStart] [date] NOT NULL,
[PeriodEnd] [date] NOT NULL,
[SoldItems] [int] NOT NULL
) ON [PRIMARY]
INSERT INTO Quantity (PeriodStart,PeriodEnd,Quantity)
SELECT '20100101','20100115',5
INSERT INTO SoldItems (PeriodStart,PeriodEnd,SoldItems)
SELECT '20100105','20100107',2 union all
SELECT '20100106','20100108',1
The actual query is now:
;WITH Dates as (
select PeriodStart as DateVal from SoldItems union select PeriodEnd from SoldItems union select PeriodStart from Quantity union select PeriodEnd from Quantity
), Periods as (
select d1.DateVal as StartDate, d2.DateVal as EndDate
from Dates d1 inner join Dates d2 on d1.DateVal < d2.DateVal left join Dates d3 on d1.DateVal < d3.DateVal and d3.DateVal < d2.DateVal where d3.DateVal is null
), QuantitiesSold as (
select StartDate,EndDate,COALESCE(SUM(si.SoldItems),0) as Quantity
from Periods p left join SoldItems si on p.StartDate < si.PeriodEnd and si.PeriodStart < p.EndDate
group by StartDate,EndDate
)
select StartDate,EndDate,q.Quantity - qs.Quantity
from QuantitiesSold qs inner join Quantity q on qs.StartDate < q.PeriodEnd and q.PeriodStart < qs.EndDate
And the result is:
StartDate EndDate (No column name)
2010-01-01 2010-01-05 5
2010-01-05 2010-01-06 3
2010-01-06 2010-01-07 2
2010-01-07 2010-01-08 4
2010-01-08 2010-01-15 5
Explanation: I'm using three Common Table Expressions. The first (Dates) is gathering all of the dates that we're talking about, from the two tables involved. The second (Periods) selects consecutive values from the Dates CTE. And the third (QuantitiesSold) then finds items in the SoldItems table that overlap these periods, and adds their totals together. All that remains in the outer select is to subtract these quantities from the total quantity stored in the Quantity Table