How does one calculate the radius of a cone when given the total surface area

The surface area formula for a cone, given its diameter (or radius) and height, is π x (diameter / 2) 2 + π x (diameter / 2) x √ (diameter / 2) 2 + (height 2), where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is π x radius 2 + π x radius x √ (radius 2 + (height 2)