Thanks, but I'm not quite following.

I thought for a voltaic reaction to occur there just needed to be a spontaneous flow of electrons from one molecule to an atom (a reductant reduces something, and is oxidized spontaneously).

Could you explain the E = reduction + oxidation? I thought E is just the "electromotive force", which has to do with electron movement where positive electron movement is spontaneous and negative is forced (like an electrolytic cell).

E is the electromotive force or you can also have EMF which is the same.

EMF= reduction + oxidation this equation is the difference in potentials between the two half cells.

For a galvanic cell the EMF is positive whereas for an electrolytic cell its negative.

For example:

Eq. 1) Co3+ + e- --> Co2+ E = +1.82 Volts

Eq. 2) Na+ + e- --> Na(s) E = -2.71 Volts

The larger the potential the more likly reduction occurs. So looking at the two equations which one has the larger value?....

Eq.1) correct its value of 1.82 Volts is > -2.71 Volts. So the total reaction will look like this:

Co3+ + e- + Na(s) ---> Na+ + e- + Co2+

Since we reversed equation 2 then the E value will change to a positive 2.71 volts.

So your EMF will be 1.82 + 2.71 volts = 4.53 volts. Since our EMF is positive it shows to be a spontaneous reaction. I hope I answered your question.