TEA was traditionally added to counteract tailing of basic compounds caused by interactions with "activated" silanols. It is much less widely used with today's higher purity columns. Since your tailing seems to be caused by overload rather than secondary interactions, I'm not sure that the TEA would help all that much. Furthermore, the addition of TEA will very likely change the selectivity, so that the method will have to be reworked. 
Adding TEA to both the A and B solvents is a good idea, but not necessarily at the same concentration (the distribution coefficient of the TEA between the mobile and stationary phases will change as a function of organic content).
Bottom line is that addition of TEA will most likely mean reworking the whole method. A tailing factor of 1.8, while not good, is not catastrophic, particularly with a large peak. If this were my problem, and I still had good resolution, I'd choose to live with the tailing.