let 'x' and 'y' represent the numbers and x>y

sum of two numbers is 500:

x + y = 500

difference is 220:

x - y = 220

larger number is greater than 300:

x > 300

smaller number is less than 200:

y < 200

by solving the system of equations:

x + y = 500

x - y = 220

we find:

x = 360

y = 140

click here to see the step by step solution of the system of equations:

360 is bigger than 300

140 is smaller than 200

the numbers are 360 and 140.