EF=(AB-CD)/2 .

After F, FM parallel AD passes through AB in M, FN parallel BC passes through AB in N ... (briefly described below).

AM=DF=CF=BN, AE=BE, so EM=EN.

∠A=∠FME, ∠B=∠FNE. Because ∠ A+∠ B = 90, ∠ FME+∠ FNE = 90.

The triangle MFN is a right triangle and FE is the center line of the hypotenuse, so EF=MN/2.

EF =(a b-AM-BN)/2 =(a b-DF-CF)/2 =(a b-CD)/2 .