AMC 10 2014a Problem 22

In rectangle $ABCD$, $\overline{AB}=20$ and $\overline{BC}=10$. Let $E$ be a point on $\overline{CD}$ such that $\angle CBE=15^\circ$. What is $\overline{AE}$? $\textbf{(A)}\ \dfrac{20\sqrt3}3 \textbf{(B)}\ 10\sqrt3 \textbf{(C)}\ 18 \textbf{(D)}\ 11\sqrt3 \textbf{(E)}\ 20$