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 and Kupferman (2004, 2005) [1,2] combined with the time-split scheme proposed by Hao and Pan (2007) [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 (Popinet, 2018 [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 (Popinet, 2018 [4]) web site (Lopez-Herrera, 2018 [5]).