Answer
$ ((s+t)^2 + v^2)^2 =v^2 + (t-s)^2 $
Work Step by Step
We use the Pythagorean theorem:
$(s+t)^2 + v^2 = \sqrt{v^2 + (t-s)^2} \\ ((s+t)^2 + v^2)^2 =v^2 + (t-s)^2 $
Thus meets the requirements of having no square roots or fractions and all three variables.