Triangle $ABC$ is an isosceles triangle with $\overline{AB}=\overline{BC}$. Point $D$ is the midpoint of both $\overline{BC}$ and $\overline{AE}$. Triangle $ABD$ is congruent to triangle $ECD$. If the length of $\overline{CD}$ is 9 units, what is the length of $\overline{AB}$?