Why is My Polarized Plate Field Calculation Incorrect?

[LCSphysicist]

Homework Statement

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Relevant Equations

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I am a little confused why my answer is wrong... Briefly, my answer is as follow: $$P = \epsilon_{0} X E = (\epsilon-\epsilon_{0}) E; \space \space \space \space \space \space \space E = P/(\epsilon-\epsilon_{0})$$

 

[haruspex]

Homework Statement:: ...
Relevant Equations:: ...

View attachment 282969

I am a little confused why my answer is wrong... Briefly, my answer is as follow: $$P = \epsilon_{0} X E = (\epsilon-\epsilon_{0}) E; \space \space \space \space \space \space \space E = P/(\epsilon-\epsilon_{0})$$

Disclaimer: all I know about this topic is from two minutes' web search.
Are you perhaps confusing the applied field with the local field?