Let the larger and smaller parts be x and y, respectively.
According to the question:
x + y = 16........(i)
2x2 = y2 + 164.......(ii)
From (i), we get:
x = 16 - y........(iii)
From (ii) and (iii), we get:
Putting the value of y in equation (iii), we get
x = 16 - 6 = 10
Hence, the two natural numbers are 6 and 10