r + h = 37

The total surface area of a cylinder will be the sum of the lateral area and twice the area of one base. (You should be able to explain why you need twice the base.) That will be

2 pi r h + 2 pi r^2 = 1628

You have two unknowns – r and h. You have two equations. You should be able to solve.

Note: I would suggest you use substitution for this. Since you’ll be using an equation quadratic in r, I’d suggest you solve the first equation for h and plug it into the second equation. That will give you an equation with only one unknown – in this case, r. Then you can either factor it or, more likely, use the Quadratic Formula.