HMMT 2007 U23

In triangle $A B C, \angle A B C$ is obtuse. Point $D$ lies on side $A C$ such that $\angle A B D$ is right, and point $E$ lies on side $A C$ between $A$ and $D$ such that $B D$ bisects $\angle E B C$. Find $C E$, given that $A C=35, B C=7$, and $B E=5$.