The common notion is that Electromagnetic (EM) waves cannot consolidate. Contrary to that, an article [2] published by the author of this article, presented a scenario which argues that EM waves can and do consolidate. Another article [1] published by the author of this article presented one such scenario, in which consolidating EM waves generate an EM Null wave without any electric and magnetic fields, which seems to violate the Energy Conservation Principle. That article [1] resolves this paradox by introducing the novel Energy Pairs Theory, which implies that this Null wave conserves the energy as untraceable energy. This article presents another paradox manifested by another scenario of consolidating EM waves, in which the resultant EM wave contains more traceable energy than the sum of the traceable energies embedded in the consolidating waves. This scenario also seems to violate the Energy Conservation Principle, because energy seems to be created out of nothing. The Energy Pairs Theory resolves this paradox, which also significantly enhances the hypothesis presented in article [1], that the energies embedded in photons and EM waves are composed of traceable and untraceable energies.