Increased Exemption

I am being made redundant and have accepted a lump sum of around €34,000. According to the company accountant they will pay me the basic exemption of €10,160 plus the tax-free allowance according to years worked, but wil tax the other €22,000-odd. According to what I have read on the revenue's website, I am entitled to an increased exemption of €10,000 on top of the basic exemption which would leave a much smaller amount to be taxed. Who is right? It would obviously make quite a difference to me. I have no pension lump sum to affect the increased exemption.

Best Regards