Which particle has the same mass as an electron but positive charge?

The positron, and it was predicted before it was found. Paul Dirac's 1928 equation combining quantum mechanics with special relativity produced solutions with negative energy, which looked like nonsense; rather than discard them he proposed they described a particle identical to the electron with opposite charge. Carl Anderson photographed one in a cloud chamber in 1932.

That was the first antimatter, and it opened the question of why there is any matter at all. The Big Bang should have produced equal amounts, which would have annihilated completely and left a universe of light. Something tipped the balance by about one part in a billion, and CP violation is part of the story - but the amount built into the Standard Model is far too small to account for what exists.

Positrons are also in hospitals. PET scanning - positron emission tomography - injects a tracer containing an isotope that emits them; each one meets an electron within a millimetre or so, annihilates, and produces two gamma rays flying in exactly opposite directions. Detecting both and drawing the line between them locates the event, and building up millions of those lines maps where the tracer went. Antimatter annihilation is routine clinical practice.