Array formulas: nested ifs and same row calculation

There are 2 inputs: A1 and B1.

In column D, there are many types of objects A. In column B, there are many types of objects B.

Here's what the formula is supposed to do:

If (D2 is 'A1' and G2 is 'B1') then, if (E2 is bigger than F2), subtract E2 and F2 (5 - 4, in this example), otherwise subtract F2 to E2 (like what happens in line 12).

If there is no match, don't do anything and just skip the row.

I would like to do this as an array formula (Ctrl+Shift+Enter), so it would sum everything in the end.

In this example, the output would be -1, because sum(and(5-4)(2-4)) .

So far, I have the following:

{=SUM(IF((D2:D12="A1")+(G2:G12="B1");E2:E12-F2:F12;0))} 

But it doesn't work properly as I'm not sure how Excel reads the subtraction part. I want to be able to subtract the values for the row where the combination was found.