In this paper, absorption phenomena in a hollow waveguide with an inserted graded dielectric layer are studied, for the case of transverse electric (TE) wave propagation. The waveguide model aims to be applicable to a study of a potential cancer treatment by heating of gold nanoparticles (GNPs) inside the cancer cells. In our previous work, general exact analytical fomulas for transmission, reflection, and absorption coefficients were derived. These fomulas are further developed here to be readily applicable to the calculation of the absorption coefficient within the inserted lossy layer only, quantifying the absorption in the GNP-fed cancer tissue. To this end, we define new exact analytic scale factors that eliminate unessential absorption in the surrounding lossy medium. In addition, a numerical model was developed using finite element method software. We compare the numerical results for power transmission, reflection and absorption coefficients to the corresponding results obtained from the new modified exact analytic fomulas. The study includes both a simple example of constant complex permittivities, and a more realistic example where a dispersive model of permittivity is used to describe human tissue and the electrophoretic motion of charged GNPs. The results of the numerical study with both non-dispersive and dispersive permittivities indicate an excellent agreement with the corresponding analytical results. Thus, the model provides a valuable analytical and numerical tool for future research on absorption phenomena in GNP-fed cancer tissue.