KöMaL 2009 C975

In triangle ABC , the altitude drawn from vertex $C$ intersects side $AB$ at $T$. Right-angled triangles CAD and CBE are drawn on sides $AC$ and $BC$ on the outside, such that the right angles are at $A$ and $B$. Given that $AD$=$TB$ and $BE$=$TA$, prove that $\angle$ CDE =$\angle$ CED .