No trick questions with the TELEX thing, and no, you don't have an address, just some number to send it off. Finding latitude is a great thing. You can find it via the POLARIS or NORTH STAR and the sun. (But with the sun, you have to have that moment when its smack overhead) It's easier using Polaris. So you have a latitude but why stop there? Why not jot down various stars at various times? (I think the more info the better.) Jot down the moon height at various times too using the inclometer. You can use your compass to get the bearing for the particular time. Log down the time and position of each reading.
How about looking around your enviroment and see the vegetation? Is it tropical, is it more subtropical? Is it mountainous? Is the island flat? I'd take a reading of the highest point on the island and draw a map of the island as best way possible, feel the temperature of the ocean.
To find longitude, you need a good watch and know the actual time of GREENWICH. But it doesn't matter. When you send in the telex, make sure you describe wheather it is day time, night time, or best to send it off right when the sun rises, and MENTION SO that the sun just rose above the horizon. The smart searchers should put two and two together with their time and know the time difference based on your information for a rough estimate of your longitude, and they should have alot of information to find you now with latitude, longitude, map outline of the island.