An inequality about condition number and LU decomposition.

Question

Suppose $P(A+E)=LU$, where $P$ is a permutation, $L$ is lower triangular with $|l_{ij}|\le1$,and $U$ is upper triangular. Show that $$\kappa_{\infty}(A)\ge\frac{\|A\|_{\infty}}{\|E\|_{\infty}+\min|u_{ii}|}$$ Many thanks for any guidance.