It is not necessary to use 'one'.

Interested in Language
Hello.
I have a question about the word "one".
In the example: You take the long route, and I'll take the short. I have to use "one" after short or it is possible to leave it out. If it is, which version is more common?
Hope you will help me.
Regards
It is not necessary to use 'one'.
“Every miserable fool who has nothing at all of which he can be proud, adopts as a last resource pride in the nation to which he belongs; he is ready and happy to defend all its faults and follies tooth and nail, thus reimbursing himself for his own inferiority.”
— Arthur Schopenhauer
But in this example, I suppose, it is impossible to omit "one".
This glass is dirty. Can I have a clean, please?
I am not a teacher.
A (relatively well-known) lyric from the Scottish traditional song The Bonnie Banks of Loch Lomond is "You take the high road and I'll take the low road". It uses what I consider to be the most natural construction - the repetition of the word "road". However, omitting the second "road" still results in a grammatically correct sentence. The same goes for your original.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.