#### Answer

18,19

#### Work Step by Step

Consecutive whole numbers have a difference between them of 1. Therefore, we let the first whole number be $x$ and the second whole number be $(x+1)$.
Since the product of the two whole numbers is 342, we obtain:
$x(x+1)=342$
$x^{2}+1x-342=0$
$x^{2}−18x+19x−342=0$
$x(x−18)+19(x−18)=0$
$(x−18)(x+19)=0$
$(x−18)=0$ and $(x+19)=0$
$x=18$ and $x=-19$
Therefore, the first number is $18$ and the second number is $18+1=19.$