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You can try:

sage: e1.substitute({e2:e3})

If this does not work, please do not hesitate to provide a way to construct e1, e2 and e3 so that we can think about it.

You can try:

sage: e1.substitute({e2:e3})

or even

sage: e1.substitute({e2:e3, 1/e2:1/e3})

if it can help.

If this does not work, please do not hesitate to provide a way to construct e1, e2 and e3 so that we can think about it.