Difference equation in OLG framework
The following approach seems to work in this case:


look for the stead state formula of $T_t$. You can do this by taking (2.8) and the formula for $T_t$, and combine them. Then, get rid of all $t$ index:


$$ T = \frac{1-\delta}{p}\left(B - \frac{B}{1+i}\right) + \frac{T}{1+i}$$

Then, rearrange until you get $T$, the steady state formula for $T_j$. You should get:

$$ T= (1-\delta)\frac{B}{p} $$


Guess what the time indexes are, and confirm they are correct. To do this,  lag the equation for $T_t$ (so you get rid of expectations), and replace $T_{t-1}$ and $T_t$ with your guess. If the equality holds, your guess is correct. If not, try again. For example, let us assume  $T_t= (1-\delta)\frac{B_{t-1}}{p_t} $ (the correct one).


Then, the equation is:

$$ (1-\delta) \frac{B_{t-2}}{p_{t-1}} = \frac{1-\delta}{p_{t-1}}\left[B_{t-2} - \frac{B_{t-1}}{1+i_{t-1}}\right] + \frac{T_t p_t}{(1+i_{t-1})p_{t-1}} $$

After simplifying and rearranging you get:

$$T_t= (1-\delta)\frac{B_{t-1}}{p_t} $$

which is correct. 

Now, I don't know how general this method is. This is not my area of knowledge. But at least it works here.