Inclusion:  18 and 85 years, inclusive. Histologically confirmed papillary or follicular thyroid carcinoma, collectively referred to as differentiated thyroid carcinoma (DTC), that is incompletely responsive to initial surgery +/- 131-Iodine as established by anatomic imaging (CT, MRI, and Ultrasound). DTC that is not completely resectable with macroscopic invasion of tumor into cervical soft tissues and/or non-resectable distant metastases. Iodine avid residual disease, but with a sub-therapeutic level of lesional radioiodine uptake demonstrated in either a pre-treatment diagnostic scan or a previous post-treatment radioiodine scan, making it unlikely that the patient would benefit from radioiodine therapy alone. Adequate organ function, including: a) adequate renal function, defined as a measured creatinine clearance >70 ml/min/1.73 m2 or normal radioisotope glomerular filtration rate (GFR); and b) adequate hematologic function, defined as a platelet count > 50,000 cells/mm3 and an absolute neutrophil count (ANC) > 500 cells/mm3 Life expectancy of at least 8 weeks. Karnofsky performance status (KPS) > 50% Patients must have adequately recovered from the effects of any prior chemotherapy, as determined by the treating physician and study team, based in part on organ function defined above. Toxicities from previous therapies must have recovered to CTCAE v5.0 grade 2 or better. Patients with previously identified cardiac disease will be eligible, as Sodium Iodide I-131 (131I NaI) is not expected to cause cardiac dysfunction  Exclusion:  Patient is pregnant or breastfeeding. Patient is sexually active, premenopausal, and does not agree to use accepted, effective forms of contraception. Any criteria that would contraindicate radioiodine therapy or external beam radiotherapy. Patient having alimentary toxic aleukia (ATA) low and intermediate risk tumors, not meeting the guidelines for either radioactive iodine (RAI) treatment or External beam radiotherapy (EBRT). Patient with advanced central nervous system (CNS) metastatic disease, critical lesions in the hip and spine, etc. that would make RAI treatment prior to EBRT potentially harmful, with respect to worsening of disease as a result of the recombinant thyroid-stimulating hormone (TSH) stimulation. Patients having recent exposure to iodinated contrast (within 6 weeks, that could render RAI treatment ineffective).