The digits of a two-digit number add up to 12…

Step 1. The equations. The digits add to $12$, so $x + y = 12$. Adding $18$ swaps the digits, so $10x + y + 18 = 10y + x$, which gives $y - x = 2$.

Step 2. Solve. Add the two equations: $2y = 14$, so $y = 7$. Then $x = 5$.

Step 3. The number. $10 \times 5 + 7 = 57$.