Implementing a total sum with logic gates
You'll notice that your math teacher would have looked very sternly at your "equation"


  TOTAL = TOTAL + INPUT


because if \$a=a+b\$, then \$b=0\$, or something's wrong. 

What you mean is "the value of TOTAL in the next time step is the value of TOTAL now, plus the value of INPUT now". 

What that implies is a temporal variation of your circuit's state: you can't build this out of combinatorial logic alone. Something has to store the "old" total while you compute the new. 

In fact, this even kind of implies you need a clocked system, with registers (usually implemented through flipflops) holding values. 

That is really all I think I can tell you without solving your "homework" (or whatever that is) for you – this gets easier if you imagine you have an external signal "clock" that goes high whenever there's a new INPUT.