Show that the Moore-Penrose pseudoinverse is the only unique left inverse of a non-square matrix

Question

Let $A$ be an $N \times d$ matrix with $N > d$. Let $A^+$ be the Moore-Penrose pseudoinverse, i.e., $$A^+ = \left( A^T A \right)^{-1} A^T$$ We can see that $A^+$ is a left inverse of $A$ as $A^+A=I$. If $L$ is another $d \times N$ left inverse of $A$, show that $L = A^+ + E$ where $EA=0$. I honestly don't know where to start here, it isn't immediately obvious to me why this fact would be true.