Let's use the clues to narrow down the possible numbers of friends Anita has invited:
- They are more than the number of days in September, which has 30 days. Therefore, the number of friends is more than 30.
- The sum of their digits is 10. This means that the number of friends could be any combination of two-digit numbers whose digits add up to 10, such as 19, 28, 37, 46, 55, 64, 73, 82, or 91.
- The difference in their digits is 2. This means that the number of friends could be any combination of two-digit numbers whose digits are 2 apart, such as 23, 34, 45, 56, 67, 78, or 89.
- They are less than 5 dozen, which is 60 x 5 = 300. Therefore, the number of friends is less than 300.
From the clues, we can see that the number of friends Anita has invited is a two-digit number between 30 and 99 whose digits add up to 10 and are 2 apart. The only number that satisfies these conditions is 73.
Therefore, Anita has invited 73 friends to her birthday party.