There's should be a file - /Library/Receipts/InstallHistory.plist
If you use TextEdit, you can navigate there by going to the top drop-down, selecting your system disk ("Macintosh HD" or whatever), and from there "Library" should appear and you can navigate to the file.
Open the file, search for "10.13.4" (it should look like "<string>10.13.4</string>") and based on the text around that line, you should be able to figure out if it pertains to the OS update. From there, look for the line with "<date>" which will appear a few lines above it. You can probably figure out the date and time it was installed from there.
There are other ways to find this information out - to me, this seemed the easiest of the common ways to find this information out.