2003 AMC 10B Problem 13

Let $y=\clubsuit(x).$ Since $x\le 99,$ we have $y\le 18,$ so $\clubsuit(y)=3$ forces $y=3$ or $y=12.$ The two-digit numbers with digit sum $3$ are $12,$ $21,$ and $30$ ($3$ of them). Those with digit sum $12$ are $39,$ $48,$ $57,$ $66,$ $75,$ $84,$ and $93$ ($7$ of them). In all there are $10.$ Thus, the correct answer is E.