If you want to list multiple adjectives at the same "adjective level" for emphasis, you have to make it clear that they are at the same level, or it sounds like you are violating the rules of adjective order: "The only one difference" sounds just as bad to me as "the green round small lump" or "a big large sizeable dog".
Ordinarily you can repeat the article to make it clear that you're effectively starting the description over:
- The one, the only, the single, the lone, the solitary difference....
- It was a big, a large, a sizeable dog....
Otherwise if two different adjectives do actually apply at the same level, you join them with and:
- The red and green shirt
- The ragged and torn coat
In the specific case of uniqueness, it is actually common to say "The one and only" as a form of emphasis.