With your data on Sheet1, Dates in column A, Vendor in column B, and row
1 as a header.
On Sheet2 with Date require entered in A1 and Vendor required in B1,
enter in C1
=SUMPRODUCT(--(Sheet1!$A$2:$A$100<=A1),--(Sheet1!$B$2:$B$100=B1))
Sorry, forgot to add the column of data being added, which I assume is
column C on sheet1
=SUMPRODUCT(--(Sheet1!$A$2:$A$100<=A1),--(Sheet1!$B$2:$B$100=B1),Sheet1$C$2:$C$100)