NMC 1993 Problem 3

Find all solutions of the system of equations

$$\left\{\begin{aligned} s(x)+s(y) & =x \\ x+y+s(z) & =z \\ s(x)+s(y)+s(z) & =y-4 \end{aligned}\right.$$

where $x, y$, and $z$ are positive integers, and $s(x), s(y)$, and $s(z)$ are the numbers of digits in the decimal representations of $x, y$, and $z$, respectively.