In the photo, it appears that the installer put brass nipples between the tank and the flex connections. Good for reducing galvanization, but the corrosion may cause the nipples to become brittle and the threads could break off if you try to remove them. Both nipples have water around them as well as old water marks on the top of the tank. A leak at both is uncommon and I would look at a possible leak from the tank into the jacket around it or deterioration from the anode finally made it to the outside of the tank.
As said before, if the tank is 10+ years it might be time for a replacement. If you do replace it, have dielectric connections to the supplies. Also, if you have a water softener the anode will have a shorter life expectancy. Flushing and inspection of an electric tank should be an annual routine. You could get a lot of years from an electric tank with the occasional element replacement and the newer tanks are bit more efficient.