Will salary and bonus terms dictated in email correspondence with hiring manager, hold up in court?

The terms of my employment were reviewed during an email chain with the company's executive who had hiring authority. Salary increases, and bonuses were stated and timed/quantified without condition in .

Long term (10 year) employee who left and company pursued to re-hire after 10 months, while retaining all tenure. Company executive pursued me to resolve an immediate need with huge financial impact on the organization. All terms were spelled out in the email on salary increase amounts, bonus amounts, and dates of effectiveness.

Negotiations were with the executive director of the product line who had hiring and negotiating authority.

Company is willing to meet a percentage, but not match the offer extended that resulted in vacating a higher paying position.