An important point is that price is only one matter that needs to be agreed.
As
@pentel says one option to consider is whether the company buys the shares not the other shareholder. There are certain rules to follow such as the company having the funds to pay and the accountant writing to advise that the payment can indeed be made out of 'distributable funds'.
Other matters are whether you are to be subject to some form of trading bar out, and whether there are to be any indemnities and/or waivers in relation to past actions/decisions , whether past interim dividends are to have approval finalised by Resolution before finalisation of the sale, whether you should receive additionally a share of the balance of dividends part paid as interim dividends, whether payment is to be in stages. whether there should be warranties from you , agreement to release you from bank guarantees etc etc . No agreement on any issue should be reached without agreement on all. Some elements can impact on price.. You want to avoid reaching an enforceable 'agreement' when important other matters that impact on price are still to be agreed. Simply signing a Stock Transfer form is dangerous. All comms should be Subject To Contract and if there has been a dispute in the background, "Without Prejudice".
There may be tax issues that can be impacted by doing things differently, For example, if you have been mistreated as employee and have a potential Tribunal claim (often linked to a split) , you could agree a compensation payment that , if no more than £30,000, will be tax free. There might also be actions the buyer would like you to do such as in relation to passwords eg for the hosting and email accounts as well possibly transferring any Intellectual Property that maybe in your name (eg if you built the website before your co-shareholder joined the company.
Finally you need to understand if there are any provisions in the Articles or Shareholders Agreement that need to be taken into account/acted jupon.
So yes you need more than a financial advisor.