1. Antioxidant – Reduces oxidation to prevent the formation of free radicals which may be harmful to health.
2. Binder / Stabilizer – Retains the physical characteristics of food/cosmetics and ensure the mixture remains in an even state.
3. Preservative – Prevents and inhibits the growth of unwanted microorganisms which may be harmful
Disodium EDTA (E386) primarily works as a preservative, chelator and stabilizer, but has also been shown to enhance the foaming and cleaning capabilities of a cosmetic solution.
As a metal chelator, it counteracts the adverse effects of hard water by binding with heavy metal ions contained in tap water, which in turn prevents the metals from being deposited onto the skin, hair and scalp. This makes it a particularly useful ingredient for rinse-off products that inherently require water to come into contact with the skin. Essentially, this ingredient deactivates the metal ions through bonding with them, which in turn prevents cosmetic products from deteriorating, maintains its clarity and prevents it from smelling rancid. Disodium EDTA can be found in various personal care products including facial moisturizer/lotion, sunscreen, anti-aging treatment, cleanser, shampoo/conditioner, hair dye, body wash and eye cream. 
This is an Unapproved E-number (E386).
Recent Findings :
In a study where Disodium EDTA is complexed with iron to increase iron bioavailability in human diets, EDTA has shown minimal toxicity where “EDTA compounds are poorly absorbed in the gastrointestinal tract and do not undergo significant metabolic conversion”. 
EDTA itself may show some genotoxicity as it has produced adverse reproductive and developmental effects in animals. However, when EDTA is complexed to a metal as a salt, such as in the form of Disodium EDTA, tetrasodium EDTA or dipotassium EDTA, to be used in cosmetic formulations, it “would produce systemic exposure levels well below those seen to be toxic in oral dosing studies” and that “clinical tests reported no absorption of an EDTA salt through the skin.” 
However, care should be exercised when taking Disodium EDTA as it is also a strong chelator (a compound that binds strongly to a metal ion) of calcium. Excess consumption of Disodium EDTA can cause hypocalcaemia resulting in cardiac arrest. 
Overall EDTA may cause reproductive toxicity as a standalone chemical, but when complexed to a metal such as in the case of Disodium EDTA, it is unlikely to be absorbed through the skin and if swallowed, will tend to pass harmlessly through the gastrointestinal tract. For those taking calcium supplements, please consult your physician before taking Disodium EDTA in excess.
Scientific References :
1. PubChem: https://pubchem.ncbi.nlm.nih.gov/compound/6049
2. Safety assessment of iron EDTA [sodium iron (Fe(3+)) ethylenediaminetetraacetic acid]: summary of toxicological, fortification and exposure data (Food Chem Toxicol. 2000 Jan;38(1):99-111)
3. Final report on the safety assessment of EDTA, calcium disodium EDTA, diammonium EDTA, dipotassium EDTA, disodium EDTA, TEA-EDTA, tetrasodium EDTA, tripotassium EDTA, trisodium EDTA, HEDTA, and trisodium HEDTA. (Int J Toxicol. 2002;21 Suppl 2:95-142 DOI: 10.1080/10915810290096522)
4. Deaths resulting from hypocalcemia after administration of edetate disodium: 2003-2005 (Pediatrics. 2006 Aug;118(2):e534-6 DOI:10.1542/peds.2006-0858)