Find a vector equation for the intersection of the surfaces x^2+y^2=25 and z=x+y. (Hint: What is the geometric object described by x^2+y^2=25? How can you write that in parametric form?)

I realize that x^2+y^2=25 is a circle, and I'm pretty sure I have to solve for one of the variables in the second surface and substitute into the first surface, but I don't know where to go after that. Any help would be greatly appreciated!