The authors analyse the self-energy operator of the Dyson equation in solids in comparison with the Kohn-Sham local potential of the density-functional theory (DFT). This allows the authors to explain why there is little difference between the DFT one-particle spectra and the spectra of actual one-electron excitations (OEE) in metals and why this difference is considerable in insulators. They can identify the terms responsible for this difference. This allows them to propose a very simple method for deriving the OEE spectra from the DFT calculation. In particular, the calculations of the energy gaps in semiconductors (C, Si), large-gap dielectrics (Ne, Ar, Kr) and ionic solids (MgO, LiF, NaCl) provide an agreement with experiment well within 5%, as well as the pressure dependence of the gap in Xe up to metallisation. The calculational effort involved is little different from that required in the usual self-consistent DFT calculation.