As you do not provide us with more information about where the chord is within the song etc. there are only two things that come to my mind.
Paul, being a bass player, or the person who transcribed or created the sheet could have referred to the base that should play a lick in parallel 10th. That was very common in these days (60's/70's), especially when going V -I, like G7 - C:
10th: B___C___C#__D -> E
root: G A A# B -> C
but even in different contexts...
But what I also noticed when listening to the song on YouTube, is that there is one chord that holds a 'minor' and a 'major' third at the same time ( which was often used in Beatles songs not so well known) and he is 'correctly' referring to this chord as C(-10).
You can not interpret this chord as C(#9) because then it would also include a b7 in the chord. And usually the #9 is one octave higher than the 3rd is in because of #9 being identical to b3 !!! So the voicing usually is
So what he definitely wants is a D chord with a major and a minor third at the same time, in the same octave, no 7th involved and with the root note as the base note, which you best jot down as
D(-10) or D(b10)
That is, because D-major(b3)/D-major(m3) or D-minor(M3) would really be confusing ;-)
Of course, you could say (add) but this is usually used for (add9) etc. -> (add9#) which actually means (add2#) would be as confusing as (add3b) or something alike!
If you are a guitar player this notation may have not crossed your way until now but if you are an arranger or coming from the keyboard this is common practice!
So at the end of the day (-10) is the most elegant solution, even if it is one of the few exceptions where an even number is used for a tension - but it definitely IS a tension, as you can hear...
EDIT: Just to clarify - A Dominant 7th chord with a #9 never lets you in doubt of the basic gender of the chord, it definitely is major. So the #9 is the correct notation. If you notated a (-10) chord as anything else than (-10) it would strongly cover the fact that this chord is all about NOT knowing or wanting to know whether the basic gender is major or minor. That's what this chord wants to convey - ambiguity...