T(3r-y)/(y^3+√r)=4 make r the subject if the equation
T(3r-y)/(y^3+√r)=4
3Tr - Ty = 4y^3 + 4√r
3Tr - 4√r - (4y^3 + Ty) = 0
This is just a quadratic in √r, so you can use the quadratic formula:
√r = [4±√(16+12y(4y^2+T))]/(6T)
Not sure just where you want to take this.