PbSe quantum-dot solids are of great interest for low cost and efficient photodetectors and solar cells. We have prepared PbSe quantum-dot solids with high charge carrier mobilities using layer-by-layer dip-coating with 1,2-ethanediamine as substitute capping ligands. Here we present a time and energy resolved transient absorption spectroscopy study on the kinetics of photogenerated charge carriers, focusing on 0-5 ps after photoexcitation. We compare the observed carrier kinetics to those for quantum dots in dispersion and show that the intraband carrier cooling is significantly faster in quantum-dot solids. In addition we find that carriers diffuse from higher to lower energy sites in the quantum-dot solid within several picoseconds.