How to solve this trig problem?

I have a hard time with solving this problem. I know that the answer is a(1-e cos E).
I also know that b^2 = a^2(1-e^2)

a^2 (cos E - e)^2 + b^2 sin^2 E =

a^2 (cos^2 E - 2 *e cos E + e^2) + (a^2 (1 - e^2)) sin^2 E =

a^2 cos^2 E -2ea^2 cos E +e^2a^2 + a^2 sin^2 - a^2e^2 sin^2E =

a^2 (cos^2 E + sin^2 E) - 2ea^2 cos E + e^2a^2 - a^2e^2 sin^2E =

a^2 - 2ea^2 cos E + e^2a^2 - a^2e^2 sin^2E =

a^2 - 2ea^2 cos E + e^2a^2 - a^2e^2 (1-cos^2 E) =

a^2 - 2ea^2 cos E + e^2a^2 - a^2e^2 + a^2e^2 cos^2 E =

a^2 - 2ea^2 cos E + a^2e^2 cos^2 E = Here I get stuck

I have tried everything but nothing seem to give the correct answer: a(1-ecosE).
What am I doing wrong?

Try the law of cosines, or maybe
the law of sines, or maybe
both.