How can I tell the time that a photo was taken, if I just have the DSCN****.JPG file?

I have some digital photos that were taken with a Nikon E4500 camera. The photos were taken by someone else and the files were copied onto my computer. They are in the jpeg format and have names like DSCN0001.JPG. I would like to know the date and time that the photos were taken, but the creation time of the jpeg file isn't helpful - it appears to be either the time that the images were downloaded from the camera, or a random time like Jan 1, 2002.
Is the true creation time embedded somewhere in the jpeg file? If so how do I get it out? I can use either linux or windows, or maybe Nikon has some useful software?

I installed the Nikon Capture NX software, but can't figure out how to use it to find the date and time that the photo was taken. Any advice? Thanks!

With dates like "Jan 1, 2002", it looks like the pictures were taken without setting the camera's date and time. When that happens, the settings show as the factory defaults (always Jan 1, and usually a year prior to 2005) and a correct date can't be determined because the EXIF data relies on the user to set the correct time.

Yeah. Look at the property of the file. As long as your camera's date and time is set correctly during the shot time, then the files should be correct too. You can use WIndows Explorer to sory by Date/Time on the most far right,

Use Nikon capture, the software allows you to have all the details on the picture taken.