From the known AC=BC
Angle CAB= angle CBA
AD=BD
Angle DAB= angle DBA
So angle DAE= angle DBF
Angle DEA= Angle DFB = 90°.
AD=BD (corner edge)
So DE=DF
Because angle C= angle E= angle F= angle EDF.
CEDF is square.
DE=CE=AE+AC=AE+BC
So ED=AE+BC