The energy of a graph $G$, denoted by ${\cal E}(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. In this paper we study the difference of energies of a (regular) graph $G$ and its complete graph $\overline{G}$, that is, ${\cal E}(G)-{\cal E}(\overline{G})$. In particular, we provide the answer to Problem 12 raised in Nikiforov (2016). Moreover, we give a lower bound for the energy of a regular graph in terms of the order and the clique cover number.