Let's say the first number is x.
The second number is then 5/8 greater than x, which is x + (5/8)x = (13/8)x.
The sum of the two numbers is x + (13/8)x = (21/8)x.
Twice this sum is equal to 22 1/4, or (45/2), so we have 2 * (21/8)x = (45/2).
Multiplying both sides by 8/21, we get (8/21) * 2 * (21/8)x = (45/2) * (8/21).
This simplifies to 2x = 4 * 45/2.
Simplifying further, we have 2x = 90.
Dividing both sides by 2, we get x = 90/2 = <<90/2=45>>45.
So the number is 45.