Question 146233
a
a+1

{{{1/a - 1/(a+1)=1/12}}}
{{{(a+1-a)/(a(a+1))=1/12}}}
{{{1/(a(a+1))=1/12}}}

This implies

{{{(a(a+1))=12}}}
{{{a^2+a-12=0}}}
{{{(a+4)(a-3)=0}}}

Gives a=-4 or a=3, a must be positive so we exclude -4 from the answer set.
So the numbers are 3, 3+1=4

Now, check:
1/3 -1/4=4/12 -3/12=1/12.