Typed it up into Anydice.

function: sum plus difference of A:n and B:n {

C: [absolute A - B]

result: A + B + C

}

output [highest 1 of 2d20]

output [sum plus difference of d10 and d10]

Turns out, it is really similar to having advantage in DnD 5e, aka Higher 1 of 2d20 (image is the same graph as above, with "at most" selected). If on the advantage though, you "rounded up" odds to evens, it is the same.

I had hoped that this would have resulted in an upper bell curve, seen below in green. Blue is the standard 3d6 bell curve for comparison.