There is, actually- just one temperature to be precise. You can prove this mathematically using the formula that converts Fahrenheit to Celsius.

First, let the Fahrenheit temperature be F, and the Celsius temperature be C.

The formula is F = 9C/5+32.

We want a temperature where F= C

So now we have C = 9C/5+32, or

5C = 9C + 160

4C+ 160 = 0

4C = -160

C = -40

F = C = -40.

So, as a few people have said, - 40 degrees Fahrenheit is the same as - 40 degrees Celsius, and there is no other temperature where this is true.

The mathematical technique for solving this is known as "simultaneous equations", where basically you have two equations that must be "simultaneously" correct.