"Opposites" cannot mean additive opposites since, by definition, their sum must be 0.
So "opposites" is likely to mean multiplicative opposites.
This gives the equation x + 1/x = 100
Then
the two numbers are 0.010010 and 99.989999 to 6 dp.
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change the sign and do the opposite operation.
99 and -99
36 and 64
103
An example of two numbers which add together to make 100 are 47 and 53.