You have a couple options. Hopefully you have a good agent because you need to get yours under contract soon. You can talk with a lender to see if you can qualify for another loan to buy the new house before you sell the old one. You will have two mortgage payments until you do. You can also make a contingent offer on the new house which means you have to sell the old one before you can buy the new one and the seller will wait for you to do it. Most sellers won't accept that unless you include a kick out clause and this is where a good agent can help. The seller will insist your old house be listed for sale with a Realtor to give it the best chance of selling.
Talk to your Realtor - we know how to do these things.