Selected Answer
You might try something like this:
=IF(COUNT(D3:E3),F2-D3+E3,"")
COUNT(D3:E3) returns 0 if both cells are blank in which case the formula writes a null string.
For some reason I don't recall I found this unsuitable in a project I did a while ago and I opted for conditional formatting. Say, the balance is in column F, apply a condition like =F3=F2 and format the font colour as white (same as cell background). The balance would still be in the cell and can be used for further calculations on the right but it would be invisible.
The drawback of this method might be that the font color is also changed when two susequent cells are blank. If necessary the formula might be expanded to check for blanks.