Olympiad Geometry · Hard problem

In $\triangle ABC$, $D$ is on $\overline{AB}$ and $E$ is on $\overline{AC}$, with $\overline{DE} \parallel \overline{BC}$. The perimeter of $\triangle ADE$ is $20$ and the perimeter of $\triangle ABC$ is $50$. If $BC = 18$, find $DE$.