Genesis 2:10 clearly states a river flowed "out of Eden to water the garden." If the river flowed "out of Eden" to water the garden, was the garden inside Eden or outside of Eden?
Your confusion is the result of the rendering in your English translation. The original Hebrew does not create this confusion.
Looking at Genesis 2:10 we find:
Gen. 2:10 Now a river flowed out of Eden to water the garden; and from there it divided and became four rivers.
A better way to render this verse in English would be, "Now a river watered the garden in Eden, and the river flowed out of Eden and became four rivers." So the Garden was in Eden, and a river originated in the garden. It eventually flowed out of Eden. You might find our Genesis Bible study helpful.