The NUMEN project aims at accessing experimentally driven information on Nuclear Matrix Elements (NME) involved in the half-life of the neutrinoless double beta decay (0νββ), by high-accuracy measurements of the cross sections of Heavy Ion (HI) induced Double Charge Exchange (DCE) reactions. Particular attention is given to the (18O,18Ne) and (20Ne,20O) reactions as tools for β+β+ and β-β-decays, respectively. First evidence about the possibility to get quantitative information about NME from experiments is found for both kind of reactions. In the experiments, performed at INFN - Laboratory Nazionali del Sud (LNS) in Catania, the beams are accelerated by the Superconducting Cyclotron (CS) and the reaction products are detected the MAGNEX magnetic spectrometer. The measured cross sections are challengingly low, limiting the present exploration to few selected isotopes of interest in the context of …