imc

$AB=EC$ because they are opposite sides of a square. Also, $ED=DC=AB$ because all sides of the convex pentagon are of equal length. Since $ABCE$ is a square and $△CED$ is an equilateral triangle, $\angle AEC=90$ and $\angle CED=60.$ Use angle addition: $$\angle E=\angle AEC+\angle CED=90+60=\boxed{150}$$