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