, 2020

We are given that $s$ and $t$ are positive integers and that $s(s-t) = 29$.
Since $s$ and $t$ are positive, then $s-t$ is less than $s$.
Since $s$ is positive and 29 is positive and $s(s-t)=29$, then $s-t$ must also be positive.
Since 29 is a prime number, the only way that it can be written as a product of two positive integers is $29 = 29 \cdot 1$.
Since $s(s-t)=29$ and $s > s-t$, then we must have $s = 29$ and $s-t=1$.
Since $s=29$ and $s-t=1$, we obtain $t=28$.
Therefore, $s+t=29+28=57$.