bob:  when I am your age      bill: when I was your age

BILL          x+d             x+2d=36                     x

BOB          x                 x+d                        x-d=3

The other person is WRONG. No surprise there!!
Bill is NOT 23, and Bob is NOT 13 as he states.

Let Bill's and Bob's ages be I and B, respectively
From either of the 1st 2 sentences it can be deduced that Bill is older. 
Therefore, difference in their ages is: I - B

When Bob is Bill's age (I), Bill (I) will be I + I - B = 36____2I - B = 36 ---- eq (i)
Also, when Bill was Bob's age (B), Bob was B - (I - B) = 3____2B - I = 3____2B - 3 = I ----- eq (ii)  

2(2B - 3) - B = 36 ------ Substituting 2B - 3 for I in eq (i) 
4B - 6 - B = 36
4B - B = 36 + 6
3B = 42
Bob or 

2(14) - 3 = I ------- Substituting 14 for B in eq (ii)
28 - 3 = I
Bill (I) is: 25 years-old