Angle Bisector

In triangle $ABC$ with $AC < BC$, let $AD$ be the angle bisector ($D \in BC$) and let $K$ be the midpoint of $AB$. On the ray opposite to ray $CB$, take a point $E$ such that $\angle ACK = \angle AEC$. Suppose that $CD = CE$. Given that $AC = 12$ and $BC = 18$, find the length $DA$.