The diffusion equation for modelling diffuse sound fields was proposed some fifty years ago on heuristic principles as an extension to Sabine's diffuse field model, and still receives much attention. Recently, the authors developed the model one step further to provide the missing relations between sound intensity and sound energy. This introduces some extra terms that, in case of non-Sabine spaces (narrow or flat rooms), can be defined with the help of the boundary conditions in terms of absorption and scattering coefficients on the walls. Integrating the divergence of the stress-energy tensor across the shortest dimensions of the space leads to a propagation equation of the Telegraph type, which can be solved using finite difference time domain simulation. For the two-dimensional case (open-space), numerical results are compared to measurements in real spaces. The comparison makes it possible to evaluate the absorption and scattering coefficients by an adjustment procedure.