It is shown that reactions with one-pion exchange, reactions of meson production in the central region and reactions of nucleon-antinucleon annihilation can be good laboratories to search, in the rho+rho+ and rho-rho- channels, for the exotic resonance states E++ and E-- with I(G)(J(P)) = 2+(2+), the signs of the neutral partner of which were discovered probably in the reactions gamma-gamma --> rho-rho. Detailed estimates are presented for the cross sections of the reactions pi+p --> E++n --> rho+rho+n, pi-p --> E--DELTA++ --> rho-rho-DELTA++, pp --> n(E++)n --> n(rho+rho+)n and similar ones at intermediate energies.