Olympiad Geometry · Challenge problem

In $\triangle ABC$, point $D$ is on $\overline{AB}$ and point $E$ is on $\overline{AC}$ with $\overline{DE} \parallel \overline{BC}$. Triangle $ADE$ has area $16$, the trapezoid $DECB$ has area $20$, and $AD = 8$. Find $AB$.