I was thinking of starting a D&D 4e campaign with two of my friends. I will DM, and they will play. They are both quite new to RPGs, and I'm not very experienced as a DM. However, 2 players does not fill all roles (Striker, Leader, etc.). How do I balance the game so that it is challenging for them, but not impossible? Is it even possible to do this in a way that it still is for both the players and me?
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Party Balance is relative, and frankly, overrated.
The roles in 4e refer to things that individual characters do well. Many classes can pull double duty in a second role if needed, but the thing that you're going to notice more is the lack of actions available to them per round than anything else. This means you'll likely want to design smaller encounters, or in larger encounters either the ability to smartly fight only a small section at a time or NPC allies to tie up the lines for a while (and allow the players to feel awesome/see their impact on the battle. So long as the NPCs can't do it without them)
Since there's only the two of them and both are new to RPGs, I'd recommend working with them to make characters that somewhat complement each other. If, however, they seem to have ideas that don't really mesh let them run with it. When the process is done, look at whatever they came up with and figure out how you can work against their strengths, rather than their weaknesses. (It is OK to face them with situations that accent their weaknesses as well, just make sure they get a chance to notice this before getting stomped by it. As DM you can always make sure that they have what they need, or at least reward good/creative ideas)
Here's a list on a Role by Role basis of the various strengths and weaknesses as I have experienced them. Note that this is combat focused (out of combat tends to not be strongly influenced by role other than maybe leader healing), and that these are generalities (it is frequently possible to build a character that subverts any one of these at the expense of other things).
Keep in mind when dealing with a small group like that, you do get a few advantages as well, such as the ability to handle small encounters fairly quickly compared to larger groups. They'll also (depending a bit on how they make their characters) be able to coordinate guerrilla tactics far more easily than a large group might be able to. Outside of combat, the ability to only have to split spotlight between two characters will make your job as DM much easier.
Overall, try things out with an eye to what works well and what doesn't for your players. You should fairly quickly get a feel for what makes the game the most enjoyable for all three of you.
I play in a two-person game myself, and it's lots of fun! There's already some great advice here, so I'll try to touch on some simple things that helped our game.