Ineed
what is the missing reason in the proof

There's a lot going on, but the main thing to focus on really is the equation 
AE+EB = CF+FD

and on the equation 
EB = CF

Because the second equation (shown above) is true, we can effectively replace the "EB" with "CF" like so
AE+EB = CF+FD
AE+CF = CF+FD

Then we can subtract CF from both sides
AE+CF = CF+FD
AE+CF-CF = CF+FD-CF
AE = FD

When I subtracted CF from both sides, I used the Subtraction Property of Equality, which is the answer needed to go into the blank.