AMC 12 2001 Problem 2

Let $P(n)$ and $S(n)$ denote the product and the sum, respectively, of the digits of the integer $n$. For example, $P(23) = 6$ and $S(23) = 5$. Suppose $N$ is a two-digit number such that $N = P(N)+S(N)$. What is the units digit of $N$?

$\text{(A)}\ 2 \text{(B)}\ 3 \text{(C)}\ 6 \text{(D)}\ 8 \text{(E)}\ 9$