Led's are really current operated devices. They take a certain voltage to place them in conduction (that 2 volts you mention), but it's all current after that. Your simplest way out is to use a 2.2K resistor in series with the voltage source to limit the current. Here's a link into our Ebook that describes LED's - http://www.allaboutcircuits.com/vol_3/chpt_3/12.html
Is the incoming voltage AC or DC?
You will loose a lot of power in the resistor.
If the voltage is DC the resistor will be (38 - 2) / 0.016 = 2250 Ohms.
The nearest higher value is a 2700 Ohms resistor.
The current will be than 36 / 2700 = 0.013333 = 13.3 mA.
The power dissipated by the resistor is 0.013333 * 0.013333 * 2700 = 0.4799 Watt.
A 1 Watt resistor of 2700 Ohms will be needed for your project.
The voltage coming in is DC. Sorry I didn't specify that. Thanks for the quick replies. I appreciate also showing how you come to the conclusions that you guys came to. I absolutely love this forum. I am in the process of reading allaboutcircuits book which is awesome. I will then try to find a resistor that matches these specs. Again, I very much appreciate the quick replies.
I put a 1 watt 2.7k ohm resistor in this circuit and the resistor is still getting very hot. Would this be normal for a 1 watt resistor? If it is normal, would there be anything wrong with going with a 2 watt resistor--this would keep temperatures down right?
A resistor of 1 Watt dissipating about 0.5 Watt will get rather warm.
If you want to have less heat produced you can take a 2 or 5 Watt resistor.
The higher the power of the resistor the more the heat is spread.
The total amount of heat will be the same.
* Use a buck converter, to convert the voltage to 3.3V or a similar voltage that is closer to the LED's forward voltage, and then a smaller resistor will do the final current limiting. It depends on the priorities. This is more costly but will waste much less power and not make much heat. Here is an example of one buck converter that could do it. You need several other components like capacitors and an inductor.
* If converting power to heat is okay for you, then you could also put several resistors in series so each one only dissipates part of the power. They should add up to about 2.7K Ohms.