Finding possible numbers to yield a certain arithmetic mean (average)

Question

I'd like to know how I could find the possible numbers to yield a certain average number (arithmetic mean), given that:

• the arithmetic mean will be calculated from 20 integer numbers, each having a possible value between 18 and 30

• 7 of said numbers are known and their sum is 180

• the arithmetic mean should be comprised between 28 and 30

Thank you