I assume that you meant 73 more cheeseburgers were sold than hamburgers.
THEN: Let h = number of hamburgers and c = number of cheeseburgers
Then h + c = 623
Since c is equivalent to h + 73, we can write that h + h + 73 = 623 and solve this equation:
Combine like terms and: 2h + 73 = 623
Subtract 73 from both sides and 2h = 550
Divide both sides by 2 and h = 275 hamburgers