We present direct measurements of the absolute energy distribution of relativistic electrons generated in intense, femtosecond laser interaction with a solid. Cherenkov emission radiated by these electrons in a novel prism target is spectrally dispersed to obtain yield and energy distribution of electrons simultaneously. A crucial advance is the observation of high density electron current as predicted by particle simulations and its transport as it happens inside the target. In addition, the strong sheath potential present at the rear side of the target is inferred from a comparison of the electron spectra derived from Cherenkov light observation with that from a magnet spectrometer.