In general, you only need a license for something you redistribute. Eclipse is "just" a development environment and CarbideJ seem to be as well. It is unlikely that they will be distributed with your application, so you are unlikely to run into trouble by using those to develop your software.
You may need to worry about the license if your application *includes* classes from either product.
In any case, both products come with licensing terms, read those (or have a lawyer read them) if you want to know what you can and cannot do.