Negative sign in general transistor current equation
Using the "Standard Referencing Method" for circuit analysis, the current through any terminal on an electrical component is measured going into the terminal like this:







simulate this circuit &ndash; Schematic created using CircuitLab

Now KCL (Kirchoff's Current Law) states that the sum of the currents into a junction like this equals zero, like so;

Ic + Ib + Ie = 0

Now we can rearrange to get Ie;

Ie = -(Ic + Ib)

This makes perfectly good sense since if the currents didn't balance out it would mean that current was entering or exiting the transistor through thin air.

It might seem counter-intuitive to reference the emitter current in the opposite direction to the one it would typically be positive in, but this is actually a very useful way of referencing currents because it avoids ambiguity, you know that the current is always referenced into the terminal.