How can I get a GED at 16 in Tennessee? ?

It seems as though 18 is typically the age of when a student may choose to quit high school in TN.  One such website mentioned, however, that TN might also provide "other exceptions that permit students with disabilities and some other students age 16 or 17" to quit school.  Please talk with your school counselor for more specific info.

If you're having difficulty with academics (and/or the school environment, in general), for instance, perhaps you may talk with both your school counselor and parents about getting tested by the Child Study Team (cst).  The cst usually includes a school social worker, learning disabilities teacher-consultant (LDT-C), and school psychologist.  That team of education professionals may provide testing to students with a suspected learning or education-related disability.  The cst will need your parents' permission before testing may begin.  

Even if the cst wants to "classify" the student (as having a type of emotional or education-related disability), that student does *not* necessarily have to be placed in special education classes.  However, placement in special ed or slower-paced classes may be an option, which may be less overwhelming for the student.  

The student who has been "classified" (by the cst) should also be eligible for reasonable accommodations," such as those permitted by the Americans with Disabilities Act (ADA) of 1990.  Such classroom accommodations may include getting longer time on tests and/or a separate room for exams (though, usually with a test proctor).  It's a possibility that if you have the right classroom support, for instance, that perhaps you'll feel as though you'd like to complete high school and fulfill the requirements for a high school diploma. 

If having been "classified" (by the cst), a written IEP (individualized education plan) would most likely be formulated with certain educational and developmental goals for the student based on the test results from the cst.  The IEP should allow for classroom accommodations.  Just an fyi that for students without having been "classified" (by the cst), medical documentation of having some type of disability should be needed to try to get classroom accommodations too.

For those eligible to take the GED (general educational development) test, it's generally recommended to take GED classes to help with studying for the GED test.  Such classes may be offered through the local community college or "county" public vo-tech school, which may help with passing the test that is necessary to obtain a GED certificate.  

This website has more general info re: the GED and the four (4) subject areas (and one may take each of the four tests separately):

https://ged.com/about_test/test_subjects/

The aforementioned site has FAQs (frequently asked questions) about the GED test, including GED test fraud:

https://ged.com/faq/

Here is a website to search for various careers, including their general requirements and "how to become one":

https://www.bls.gov/ooh/ and can click the "occupation groups" of interest or type into search for whichever career that piques one's interest.

The following website has U.S. community colleges, which not only may offer GED classes, such as in the "non-credit" or "continuing education" listing, but community college may also offer job or career-oriented certificate programs and Associate (two-year) degree programs, especially for those with a high school diploma or GED certificate:

https://www.aacc.nche.edu/college-finder/

For anyone who is feeling suicidal, here is a toll-free 24/7 helpline:

1-800-273-TALK (8255).

If dealing with mental health (and/or addiction) issues, this website should have some local counseling agencies (which may include one's parent making the appointment):

https://findtreatment.samhsa.gov/

Their toll-free 24/7 ** referral ** hotline:

1-800-662-HELP (4357).

GED in Tennessee

Tennessee’s Department of Labor and Workforce Development is responsible for the state’s high school equivalency testing program.

Tennessee is using the HiSET exam for this purpose.

Minimum Age for Testing – 18

17-year-olds may also qualify if they have an age waiver form signed by the Director of Schools and if they partake in a state-approved HiSET Option Program. Sixteen-year-olds cannot take the HiSET in Tennessee.

There is no state residency requirement in Tennessee.

From bestgedclasses.org

You can't AND it would involve you passing courses which you say you are failing.

You can't.  You have to be 18, or 17 with additional permissions and requirements that must be met. 

what does your state's department of education website say?  you can search this out as well as we can.  I know that, in my state [Florida], you can't leave school before age 17 unless A) you are 16, AND B) you have mother's permission to do so on form, AND C) school board approves.  I am told, but have no experience proving it, that C) will NOT be granted for any student on an IEP.