Did you have a City permit to build the patio? Did you have a survey done when you built the patio? Did the City give a sign off on inspection after the patio was built?
These would all be points in your favor to argue about.
More detail is needed.
And and expert on side-yard setbacks vs. rear-yard setbacks may be needed.
Get an attorney involved. Here are some of the things that could happen:
1. If you find the survey you should have gotten when you bought the house. and if the patio is shown on it as being within your property line, you may have to take action to prevent the neighbor from attempting to build the fence until the property line dispute can be resolved.
2. If you don't find the survey or if you do and the patio is NOT on it, you may need to get a new survey and have the surveyor "spot" the patio to see where it ends. Depending on what the surveyor determines, you may wind up in the same situation or discover that whoever put the patio in put it in the wrong place and your neighbor may be right.
3. Even if you find the building permit for the patio, it could have been installed improperly or the municipality could have made a mistake (usually in order to get a permit you must present a survey and show where the patio would be put in, but contractors can make mistakes too) and then again it may have been installed without a permit.
4. 18 years is a long time but not quite long enough to give you rights of adverse possession, and in any event that implies some kind of litigation to resolve the issue.
5. Assuming your property is "lot and block" -- ie. part of a staked subdivision and not necessarily one defined by "metes and bounds" it may be easier to determine where your real property line is - especially if you can locate iron stakes at the corners, although some owners and contractors have been known to remove them especially when installing fences at the property lines.....