Express each of max(x,y) and min(x,y) in terms of abs function.

Start at the midpoint, and then either add or subtract half the absolute difference

min(x,y) = (x+y)/2 - abs(x-y)/2

max(x,y) = (x+y)/2 + abs(x-y)/2

Simplifying,

min(x,y) = (x+y - abs(x-y))/2

max(x,y) = (x+y + abs(x-y))/2