Can I sue the primary borrower of a student loan if I'm stuck paying off the loan I co-signed for?

Letters such as this one can be considered a contract that can be enforced, however a review of the content of the letter would need to be analyzed. Keep in mind that a claim for breach of contract has a statute of limits which means you need to file suit within a certain time period. Every state has different deadlines. Keep in mind also that the legal effort needed to be expended may be worth more than the amount of the claim. Accordingly you may want to consider suing them in small claims court. Discuss with counsel in your state about these and other legal options.