The answer is $\boxed{18}$

By the Pythagorem theorem, it can be show that $BE=6$. Then, extend $BE$ to point $F$ such that $AF\perp BF$ as shown. Then $\triangle{BEC}\cong \triangle{AFB}$. It follows that $AF=BE=6$.

Now, for $\triangle{ABE}$, use $BE$ as the base and $AF$ as altutide, then its area is $18$.