An experimental setup that allows quantitative measurements of the temperature programmed desorption of different gases from any sample is described. The samples to be analyzed are uniformly heated to temperatures up to 2100 K by electron bombardment from the rear side at a rate of about 10 K/s. The temperature is controlled and can be measured on the front side by a pyrometer. The gases released from a sample are measured with a quadrupole mass spectrometer according to the partial pressure change in the residual gas. In order to get quantitative results the equipment is calibrated for different gases. The facility was tested with measurements of the hydrogen inventory and desorption temperatures for graphite samples from the vessel walls of the fusion experiment ASDEX Upgrade.