You can do a pretty rough calculation to see if you’re likely to be approved for the size of mortgage you’d need.
Estimate how much the house is worth now - go on Zoopla and look at sold prices in your road/local area.
Subtract the amount of the mortgage remaining to pay.
E.g. £250,000 (house value) - £150,000 (mortgage outstanding)
= £100,000 (equity)
Now you have the equity figure divide by 2 (50% each = £50,000 equity each). As PPs say, you can agree this to be a different split but if I were you I’d start at what the max you’d need to pay is.
So you need to pay ExH his £50,000 AND take on the remaining mortgage yourself. So in my example, that would mean you’d need to be approved for a total mortgage of £200,000.
You can’t buy him out with a loan from another lender as your mortgage company won’t allow that.