We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman [1, 2] combined with the time-split scheme proposed by Hao & Pan [3]. The use of such a time-split scheme has been proven to increase the stability of the numerical computation of two-phase flows. We show that the adaptive computational technique can be used to simulate viscoelastic flows efficiently. The solver is coded using the open-source libraries provided by the Basilisk [4] platform. In particular, the method is implemented for Oldroyd-B type viscoelastic fluids and related models (FENE-P and FENE-CR). The numerical scheme is then used to study the splashing of weakly viscoelastic drops. The solvers and tests of this work are freely available on the Basilisk [4] web site [5].