Tribal Social Security Fairness Act of 2018 (Sec. 2) This bill directs the Social Security Administration, at the request of an Indian tribe, to enter into an agreement with the tribe for the purpose of extending Old Age, Survivors, and Disability Insurance benefits under Social Security to tribal council members. In addition, the bill allows tribal council members to receive Social Security credit for taxes paid prior to the establishment of the agreement, if the taxes were timely paid in good faith and not subsequently refunded.