How do you solve for individual currents and voltages?

The image that you provided in your link shows a circuit with a total current of 10 Amperes and a total resistance of 48.766 Ohms.

Using V=IR with these two values gives a battery voltage of 487.66 Volts.

The method of equivalent circuits would be the easiest approach to analyzing this circuit, since it only involves resistors. In this method, we can redraw a circuit with groups of resistors replaced by their equivalent resistance. Thus, in your example, one possible equivalent diagram to the one you gave is a circuit with three resistors in series:

R1 = 12 Ohms

R2 = 20 Ohms

R3 = 16 + (128/167) Ohms

Ohm's law (V=IR) can then be used across each equivalent resistance to get more information about voltage drops and currents.

One then constructs another equivalent diagram that only replaces certain resistor groups with their equivalents, and then repeats the Ohm's law analysis to get more information.

This process is repeated until everything is known about the original circuit.

Alternatively you might also look into Kirchoff's rules for circuits:

1) In any closed loop in a circuit the sum of all voltage drops and rises must equal zero.

2) At any junction in a circuit the sum of the currents going in must equal the sum of the currents going out.

These two rules will allow you to set up a system of linear equations that describe the circuit. The system of equations can then be solved using standard mathematical techniques (algebra in this case).

I hope that this helps.