Electromagnetic characteristics of the E-plane T-junction for two rectangular waveguides using resonant coupling between the waveguide sections were studied by mathematical modeling. The problem of coupling between infinite and semi-infinite rectangular waveguides through a resonant slot in the end-wall of the semi-infinite waveguide in the presence of resonant monopole is solved in a strict electrodynamic formulation. The monopole with variable surface impedance is placed parallel to the narrow walls at an arbitrary position inside the infinite waveguide. The problem is solved analytically by the generalized method of induced electro-magneto-motive forces. Impedance vibrator inclusions with variable electro-physical parameters have been analyzed as control elements for waveguide junctions. To this purpose energy characteristics of the junction in the single-mode regime of the both waveguides, and also in multi-mode regime of the semi-infinite waveguide is investigated. The results may be useful for development of variety antennas and waveguide devices, which involves waveguide junctions.