How can I straighten my teeth if I've already had 10 years of orthodontia?

Second opinion. It might be time for a second opinion. There are many approaches to orthodontic therapy. If your situation has not been resolved after ten years of treatment it is probably time for a different approach.
Caution. Your situation is thankfully quite rare. The average duration of orthodontic treatment is 2-3 years. Seeking a second opinion with a licensed orthodontic specialist would be a first step to determine what more treatment you could even require.
Re-evaluation needed. If you've had braces before but your teeth have relapsed and are no longer as straight as they were after your braces were finished, you may need some type of orthodontic treatment again. There are several possible ways to treat this relapse depending upon the severity of your problem. Please contact your general dentist or orthodontist and set up an appointment for a consultation.
Exam with X-rays. You did not say whether you are currently in treatment or if you had treatment for 10 years in the past. In either case i would be concerned about root resorption and decay/ decalcification. Best to get current x-rays with and over all assessment of your dental health.
Easily. Previous orthodontics is not a contraindication for future orthodontics, unless you have root reabsorbtion.
Re-Rx. 10 years in an inordinately long time in ortho rx. If you are in appliances now, perhaps a second opinion is in order. If you were treated as a tween-teen, and you have had relapse, perhaps re-rx is in order. Seek the opinion of a qualified orthodontist, or ask for an opinion from a university specialty teaching program.
Health. If the health of the teeth and surrounding structures is good, orthodontics can be still done. 10 years is a long time, were you in active treatment the whole time, or waiting between phases? Having said yes. The point brought up about, why? If relapse is that ingrained, several opinions needed.