There are a few ways to do this. One way is through contrasts and the other way is through a variety of results relating to specific statistics (like 2-sample t-tests and their extension) along with asymptotic and approximate statistics.
If you are using something like SAS, you can specify a contrast that will test your hypothesis and give you a p-value (and a test statistic). The statement you use is the contrast statement.
Are you using a computer package?