$\text{Common Potential is } V = \frac{C_1V_1+C_2V_2}{C_1+C_2}$

$\text{Initial Energy is }U_i = \frac{1}{2} C_1V_1^2 +\frac{1}{2} C_2V_2^2$

$ \text{Final Energy is }U_f = \frac{1}{2} (C_1+C_2) V^2 = \frac{1}{2} (C_1+C_2) (\frac{C_1V_1+C_2V_2}{C_1+C_2})^2$

$\text{loss of energy is } \Delta U = U_i - U_f = \frac{C_1C_2(V_1-V_2)^2}{2(C_1+C_2)}$