The issue of relativistic toroidal MHD equilibrium with anisotropic pressure has been studied in past theoretically and on betatrons but there are very few applications in the tokamak world despite this topic is essential for reliable RE control and can be very useful for RE diagnostics. In the COMPASS experiments, it was shown that the RE beam equilibrium is significantly altered compared to the standard tokamak Grad-Shafranov equilibrium and the most important quantity affecting the macroscopic behaviour is the RE energy. Indeed, even a significant modification of position control for RE beam was necessary, however this in turn brought a diagnostics method based on the force equilibrium where the role of isotropic hot plasma pressure is replaced with anisotropic relativistic pressure. The important conclusion is that some of the standard EFIT output quantities can be used directly as total or average energy measure in the first approach. The evolution of such signals is discussed with respect to other diagnostics at COMPASS and briefly for JET. First building blocks of a code to calculate the possible energy-dependent RE equilibrium solutions in (R,z) plane are discussed.