The notes B# and E# (or Cb and Fb) don’t seem to exist on a piano or in music in general. Why is that?
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a couple thousand years ago, they figured out that certain patterns of notes sounded good together. This ended up being the major and minor scale. For these scales to work, there are 12 notes in an octave. They decided to make the scale that goes ABCDEFG (i.e., no sharps or flats) the A minor scale. So that’s 7 notes, with 5 other notes between them. Those end up being sharps/flats. However, in A minor, the B/C and E/F happen to be next to each other (with no extra note in between), so there is no need to have a sharp between them because there’s no room for one.
The fact it’s B/C and E/F is arbitrary, it could have been between any two notes the same interval apart, but they just decided to build around A minor and go from there.
Your premise is wrong. Both B and E sharp are on a piano and can be played. It’s the white buttons on the right of the B and the E.
They do exist. E# is just the same note as F, just like C# and Db are two names for the same note.
Now if you just want to point out one note on its own, there’s no reason to use E# over F. However, if you want to use the F# major scale, for example, you’d call its notes F#-G#-A#-B-C#-D#-E#-F# so every letter is still represented once in the scale. This makes notation easier, as you can just mark both the E and F as sharp at the beginning of the staff and then write an E whenever you’re playing a natural F and an F whenever you’re playing an F#. Otherwise you would have to switch back and forth with sharp and natural signs all the time.
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