Let the larger number be x and the smaller number be y.
Then, we have:
x + y = 137 ……….(i)
x - y = 43 ………(ii)
On adding (i) and (ii), we get
2x = 180
⇒ x = 90
On substituting x = 90 in (i), we get
90 + y = 137
⇒ y = (137 – 90) = 47
Hence, the required numbers are 90 and 47
