It looks like your cube has a subserf modifier on it, so when you joined the two, the text inherited the subserf.
The active object (the object you selected last, even if you deselected it), is the object that the other objects get joined to, so those objects also inherit it's modifiers. If you had selected one of the text objects last (making it active), it would have removed the subserf from the cube.
What can you do to fix it?
- You could apply the subserf before joining the cube and the text
- You could adjust the text so that it's subserf friendly, by adding holding edges.
- You could keep them separate. This might seem obvious, but depending on the object, it can sometimes be better to just keep the objects separate.
- As GiantCowFilms mentioned, you can also use the mean crease. Usually I don't recommend using this because it can cause distortions if it's not used properly, but in this case it works perfectly fine.