smc

If Jack's current age is $\overline{ab}=10a+b$, then Bill's current age is $\overline{ba}=10b+a$. In five years, Jack's age will be $10a+b+5$ and Bill's age will be $10b+a+5$. We are given that $10a+b+5=2(10b+a+5)$. Thus $8a=19b+5\Rightarrow a=\frac{19b+5}{8}$. For $b=1$ we get $a=3$. For $b=2$ and $b=3$ the value $\frac{19b+5}{8}$ is not an integer, and for $b\ge 4$, $a$ is more than $9$. Thus the only solution is $(a,b)=(3,1)$, and the difference in ages is $31-13=\boxed{18}$.