Why Extended Euclid algorithm? We can apply simple logic. Let's represent the number $$$N$$$ as $$$10*a+b$$$ where $$$b \lt 10$$$ and $$$M = a$$$. So we are given the number $$$X=N-M=10*a+b-a = 9*a+b$$$. We can easily see that if $$$b \neq 0$$$ and $$$b \neq 9$$$ (i.e. $$$X$$$ % $$$9 \neq 0$$$) then $$$a = X / 9$$$, $$$b = X$$$ % $$$9$$$ and $$$N$$$ can be unique restored. If $$$b$$$ is $$$0$$$ or $$$9$$$ (i.e. $$$X \% 9 = 0$$$) then for $$$N$$$ we have two possibilities: $$$10*(X/9)-1$$$ and $$$10*(X/9)$$$.