I don't see anything barring use of other numbers in exponents. Nothing explicitly says you can only use 7s. It's certainly implied that the 3 7s are the central parts so you can't do something like add or subtract a different number but you can square or cube.
Closest I can get with the more limited interpretation: 7!/sqrt(7!)รท7=10.14
Looser interpretation: (7!)^(1/5)+(7!)^(1/5)-7^0=10.003