jmc

We can line up the numbers and add just as we do in base 10. For example, in the second column we get $1+6=7$, which we carry just as in base 10 by placing the digit 0 in the sum and carrying 1 to the next column. We get \begin{array}{c@{}c@{}c@{}c} & & 1 & 0_7 \\ + & 1 & 6 & 3_7 \\ \cline{2-4} & 2 & 0 & 3_7, \\ \end{array}so the sum is $\boxed{203_7}$