Can the golden ratio accurately be expressed in terms of ee and π\pi

I was playing around with numbers when I noticed that e was very somewhat close to ϕ

And so, I took it upon myself to try to find a way to express the golden ratio in terms of the infamous values, π and e
The closest that I’ve come so far is:
φeπ(e+π)ee

My question is,
Is there a better (more precise and accurate) way of expressing ϕ in terms of e and π ?

Answer

The following is exact. 🙂

ϕ=ππ+e+e+e+e+eeee+ππ

Attribution
Source : Link , Question Author : Nick , Answer Author : vadim123

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