The man was wounded in the gunfight, but went back into the house. Officers entered the house and administered first aid.
The shot man was then taken to the Royal Sussex County Hospital in Brighton with what are described as life-threatening injuries.
Chief Inspector Jayne Dando said: "We did advise local residents to remain indoors while the incident was under way, but I would like to stress that there was little danger to the neighbouring community and this was kept to the absolute minimum.
"To contain the situation effectively it was necessary to deploy a police helicopter for some considerable time and I should like to apologise to Seaford residents who may have been disturbed by what was an essential need.
"I should also like to thank the head teacher of a local school who opened up the building to act as a rendezvous point for emergency services and also to provide shelter to a few local residents who were returning home, but unable to gain access to their houses for a little while."