You "can" do do it that way, but it would be easier to use ground. Setting it up the way you describe will require you to setup one pin high and one pin low. It's like having two light switches next to each other to control one light. You can do it that way but it's more complicated.
You also want to have a resistor. A LED is a diode, and allows electrons to flow easily in one direction. Without a resistor in the circuit you will create a short that will draw too much current and might damage something. I have seen people recommending 330 Ohm resistors for one led projects.
So add a resistor for safety, and then you set GPIO25 to output mode using:
gpio -g mode 25 out
Then set the pin to high(3.3v)
gpio -g write 25 1
As long as you have the led the right way around this will work. If you want to connect the other end to another gpio pin(instead of the GND pin right next to BCM_GPIO pin 25), you can just write 0 to that pin. Here is a picture that might help.