I think it's partly a personality thing - I have 2 older siblings and I fought constantly with one but never with the other one. Just like having a good sleeper/good eater/an easy going child, it may be partly parenting but its also luck of the draw!
If they share a room then that will not be helping matters, although I'm sure you would live in a 3 bed if you could! But if you can think of any ways to give them a bit of their own space that could be helpful.
My dcs are younger than yours (6 and 8) but we had some success with promising them a toy they wanted if they could go a whole week without fighting. It took many, many weeks before they managed it but they got there in the end and I do think it helped teach them how to communicate their frustration without lashing out as a default.
We also enrolled them both in (separate) clubs so they could have more time away from each other and be their own people a bit more rather than living in each others pockets. Fighting is always worse in the school holidays because they're forced to spend every day together.
I do come down very hard on any violence that I see between them. I can't be there 24/7 watching them though so they do need to take responsibility and come to me if its looking like hints are getting heated between them.
I think that, at their ages, pp's suggestion of having a family meeting to discuss ways to stop the fighting is a good idea. They need a chance to reflect on their actions and they might be able to come up with some decent ideas to improve things.
It's very hard being on your own with 2 kids. I am a single parent and the 1-2 days a week their dad has them is necessary for my sanity. I'm in complete awe of anyone who manages to look after multiple children without another parent to help.