As other users have mentioned, this depends highly upon the height of the plane. Having taken a few photos of a plane flying above recently, I can share with you my results. For this effort, the plane was presumably cruising (I'm in so-called flyover country). If the plane is closer to the ground, you're in a much better position than I was.
This was taken at ISO 100 at 300mm (fully extended for this lens, not exactly optimal territory).
Even at 300mm, the plane is quite small in this photo. Here is a cropping of just the plane:
I played around with settings briefly, but the data just isn't there. As a result, if you're trying to get a plane while quite high up, you'll need something significantly more powerful than 300mm. Depending on the prominence of the numbers (I can't even locate where they would be in my photo), a 600mm or more may get what you want, but even that could be difficult. Of course, if your goal is to just get the information on the plane, rather than necessarily getting a photo of that information, there much better ways to do this, as described by other users.
Assuming you already have a DSLR camera body, you could probably rent the necessary lens for the day or a weekend or such to save money if you don't need the lens afterwords.