As MCollett said, it’s just not possible. But understanding why it’s not possibleand trying the various ways that people have tried to solve the problem with a compromise in one aspect or another can lead to better understanding of topology and tessellation and how they interact.
Not using a UV sphere makes it a different problem. Icospheres unwrap without any distortion at all and polyspheres have a trivial amount, but it’s more diifficult to map the texture, especially if you are trying to use premade ones, like a map of the globe. If you plan to subsurf then the polysphere has no shading problems, followed by the UV sphere with poles patched with rectilinear grids.