We have the following congruence equation:
$$10x \equiv 8 \mod (59)$$
I was requested to solve this using the Euclidean method. First I noticed the $gcd$ of $10$ and $59$ is $1$, which means the equation will have a solution (for $1$ divides any integer). I know I'm now suppose to find that $1=10s+59t$. And this is the part I'm having trouble with: what are the values of $s$ and $t$ and how do I find them?