A ball of mass \(m\) is attached to a light string of length \(L\) and whirled in a vertical circle. At the bottom of the circle (Point B), the ball has speed \(v_B\) and the tension in the string is \(T_B\). At the top of the circle (Point T), the ball has speed \(v_T\) and the tension in the string is \(T_T\). The speeds at these two points are related by the equation \(v_B^2 - v_T^2 = 4gL\). In terms of \(m\) and \(g\), what is the value of the difference in the tension magnitudes \(T_B - T_T\)?