Reflection

We start on the left. Since $B=0$ , nothing is carried from the $D\times B$ multiplication. Thus $D\times A = D$ and $A = 1$ . Looking now to the right side, $D^2$ must end in a $1$ . Since $D\neq 1$ , we know that $D=9$ . So an $8$ is carried and $9 \times C + 8$ must end with a zero and have a $C$ carried, so $9\times C + 8 = 10C$ , which means that $C=8$ .

Thus $C+D = 8 + 9 = \boxed{17}$ .