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19 and 34.
Let the two numbers be x and y; then:
x - y = 15
x + y = 53
Adding the two equations gives:
2x = 68 → x = 34
Substituting for x in the second gives:
34 + y = 53 → y = 19
Checking by substituting for x and y in the first gives:
34 - 19 = 15 as required.
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