[en] We consider two-photon and Bremsstrahlung mechanisms for the production of two charged pions in high-energy electron (proton) scattering off a transversely polarised proton. Interference between the relevant amplitudes generates a charge-odd contribution to the cross section for the process. In a kinematics with a jet moving along electron spin-independent part may be used for determination of phase differences for pion-pion scattering in the states with orbital momentum 0 or 2 and 1 whereas in a kinematics with a jet moving along proton spin-dependent part may be used to explain the experimental data for single-spin correlations in the production of negatively charged pions. We also discuss the backgrounds and estimate the accuracy of the results at less than 10% level. In addition simplified formulae derived for specific kinematics, with small total transverse pion momentum, are given