I know how to find the emitter current of a single tranistor with Ie*(Re/Rb + Re/Rc + 1) = Vcc(1/Rb + 1/Rc) - (Vbe/Rb + Vce/Rc), but how would I find the current of this and gate with two transistors?

 

Your formula wouldn't work even if there were only one transistor. Hint -- what is Rc?

Your diagram and descriiption aren't sufficiently complete to answer the question. What are the input voltages? What is the collector of the top transistor connected to? Vcc? What is the bottom of the emitter resistor connected to? 0V? What model do you want to use for the transistors? Constant Vbe? Exponential? Do you want to take the base currents into account or neglect them?

Most analyses on transistor circuits involve reasonable approximations and simplifications, but we lack the knowledge about the context of the analysis to determine what are reasonable approximations and simplifications.

 

That's a lot better than what I was thinking. ("I don't know" seems pretty lame, so I didn't post it.)

 

It is known that the emitter current is very close in value to the collector. In some applications it is considered so.
If: Ie ~ Ic, then knowing that Ic (collector current) is given by Vcc / R (where R is a 1K resistor in the picture attached in the first post), so the maximum current is given by the ratio Ic = Vcc / R.
Knowing that and the hFe value of each transistor, then can be calculated the terminal base current of the transistors: Ib = Ic / hFe
After that, apply: Ie = Ic + Ib.
Calculation is more than satisfactory.

 

It is known that the emitter current is very close in value to the collector. In some applications it is considered so.
If: Ie ~ Ic, then knowing that Ic (collector current) is given by Vcc / R (where R is a 1K resistor in the picture attached in the first post), so the maximum current is given by the ratio Ic = Vcc / R.
Knowing that and the hFe value of each transistor, then can be calculated the terminal base current of the transistors: Ib = Ic / hFe
After that, apply: Ie = Ic + Ib.
Calculation is more than satisfactory.

No, the collector current is not Vcc/R; Vcc is not the voltage across that resistor. Depending on the value of Vcc and the value of the input voltages, that may or may not even be a close approximation.

 

The inputs voltages are all 5v. I want the exact current with no approximation.

 

No such thing as "no approximations" when dealing with circuits. In particular, you have to choose a model for your transistors and that model is only an approximation to the actual behavior of the transistor.

So, what are the parameters for the transistors? What temperature is this at? What is Vcc? What is the voltage at the bottom of the emitter resistor?