differencing op amp circuit
What you have now is an analog comparator due to positive feedback.  Diagram your circuit again, this time using negative feedback, and when you repeat the calculations you'll get much more reasonable resistor values.

(If you're copying from a textbook sum/difference amp circuit, please note that having the feedback resistor top or bottom is not important, connecting it to the inverting input pin is, and that op-amp symbols vary in placement of the input pins.  Your textbook likely drew the circuit with pin 2 above pin 3.)

Of course, with a 12V supply, your inputs will have to be chosen so that the output isn't 40V.

You might try a topology like this (resistor values are not set correctly, that's up to you):



(And for Matt's benefit, here's the solution, showing that R3 is not unnecessarily adding complication)



A nice way to analyze this is to first consider the circuit with only \$R1\$ and \$R2\$ present.  Then

$$V_{out} = (1 + \frac{R1}{R2}) V3 - \frac{R1}{R2} V4$$

If the non-inverting gain is too high, use a voltage divider on \$V3\$.  (This gives the Wikipedia circuit).

If the inverting gain is too high, use a voltage divider on \$V4\$.

Final gains:

$$G = \frac{R1}{R2 || R3} = \frac{R1 R2 R3}{R2 + R3}$$
$$V_{out} = (G+1) \frac{R5}{R5 + R6} V3 - G \frac{R3}{R2 + R3} V4$$