Bought it for 310k
Selling now for 355k
6% realtor cut will knock it down to 334k
If you have to make any concessions or credits to the buyer's for one thing or another, you are getting closer and closer back to that 310k mark.
Now, given that you only owe 248k on it, you've paid off some money on it, which really - you're simply freeing up your money/equity to use as a down payment on the new house.
Given that seems to be what you need, and that you'll be staying in the same neighborhood - I'd encourage you to explore the idea of taking out an equity loan on the house you have, using that as the down payment amount on the new home being built - and KEEP this original house and rent it out.
In 5 years you'll be able to post even better threads about having huge equity in TWO properties then.