We present the results of the analysis of eta -> e(+)e(-)gamma and eta -> e(+)e(-) decays. The experimental data were collected in proton-proton collisions at incident proton kinetic energy 1.4 GeV using the WASA detector and the COSY storage ring. We describe the extraction procedure of the eta meson transition form factor, based on a sample of around 10(8)eta mesons, and show an attempt to search for physics beyond the Standard Model that led to the setting of an upper limit on the coupling between photons and hypothetical dark bosons. We also provide an estimate of the branching ratio upper limit for the very rare eta -> e(+)e(-) decay.