As shown in the figure, make a straight line FG parallel to AB.

Because AB//CD, AB//FG

So FG//CD

So ∠B=∠ 1, ∠2=∠D (two straight lines are parallel and their internal angles are equal).

So ∠ 1+∠ 2 = ∠ B+∠ D。

That is, ∠E=∠B+∠D