An investigation on the equation of state of the is ospin asymmetric, hot, dense matter of nucleons and deltas is performed based on the relativistic mean field theory. The QHD-Ⅱ-type effective Lagrangian extending to the delta degree of freedom is adopted. Our results show that the equation of state is softened due to the inclusion of the delta degree of freedom. The baryon resonance isomer may occur depending on the delta-meson coupling.The results show that the densities for appearing the baryon resonance isomer, the densities for starting softening the equation of state and the extent of the softening depend not only on the temperature, the coupling strengths but also the isospin asymmetry of the baryon matter.