This study presents a new concept related to Energy, the concept of Energy Pairs. The study starts by trying to answer the following question: is it possible to detect the energy embedded in a Null electromagnetic wave, which is an electromagnetic wave that does not contain any electric or magnetic fields at all. The article describes how to create such an electromagnetic wave from two normal electromagnetic waves, that do contain electric and magnetic fields, which collide and following their collision consolidate and unify and continue to travel together in the same direction. In a proposed experiment of producing a Null electromagnetic wave, examined in the study, energy loss in the process was observed, which seems as a violation of the energy conservation principle. The main part of this study is the development of the "Energy Pair Theory" (EPT) that explained the above energy loss by the central idea of this theory that energies can be accumulated and stored as "Energy Pairs" that exist but disable each other, and therefore, the energy that is accumulated in the pairs exists but is undetectable or untraceable. The Energy Pair Theory, developed in this study, puts the concept of "Energy" in a new and an interesting framework that is flexible and convenient to be further used as a framework in studying other physical and natural observations.