Let the numbers be x and y
Then, xy = 120 and x2 + y2 = 289
∴ (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
∴ x + y = 

529" role="presentation" style="outline: none; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; font-size: 14.157px; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; text-align: inherit; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">529−−−√$$\sqrt{\mathrm{under\; root\; 529}}$$

  = 23