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If the given information is the sum and the product of two numbers, then the numbers are not integers, because only 1*21 or 3*7 equals 21, and their sum is different from 27. So let's write the quadratic form of an equation given the sum and the product of roots, and solve it.
The sum = 27, the product = 21
x2 - (summ of the roots)x + (product of the roots) = 0
x2 - 27x + 21 = 0; a = 1, b = -27, and c = 21
x = [-b ± √(b2 - 4ac)]/(2a) the quadratic formula
x ={-(-27) ± √[(-27)2 - 4(1)(21)]/[2(1)] = [27 ± √(729 - 84)]/2 = (27 ± √645)]/2
Thus, the numbers are (27 - √645)]/2 and (27 + √645)]/2.
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