2 of 2 added 762 characters in body

Jelly, 9 bytes

÷400⁵*÷S$

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The input is an array [Ra, Rb] and the output is an array [Ea, Eb].

Explanation

÷400⁵*÷S$  Input: array [Ra, Rb]
÷400       Divide each by 400, makes [Ra/400, Rb/400]
    ⁵*     Raise 10 to that power, makes [10^(Ra/400), 10^(Rb/400)]
        $  Monadic chain operating on previous result
      ÷      Divide each by
       S     The sum of the whole
           Makes [10^(Ra/400)/(10^(Ra/400) + 10^(Rb/400)),
                  10^(Rb/400)/(10^(Ra/400) + 10^(Rb/400))]
               = [1/(1 + 10^((Rb-Ra)/400)), 1/(1 + 10^((Ra-Rb)/400))]