Recent observations of solar twin stars with planetary systems, like the Sun, have uncovered that these present a peculiar surface chemical composition. This is believed to be related to the formation of earth-like planets. This suggests that twin stars have a radiative interior that is richer in heavy elements than their envelopes. Moreover, the current standard solar model does not fully agree with the helioseismology data and solar neutrino flux measurements. In this work, we find that this agreement can improve if the Sun has mass-loss during the pre-main sequence, as was previously shown by other groups. Despite this better agreement, the internal composition of the Sun is still uncertain, especially for elements heavier than helium. W...