Maybe the following workaround attempt
will be helpful?

var('x,mp,me')
eq=mp-sqrt(x^2+me^2)==x
assume(mp>0)
solve(eq^2,x)
[x == 1/2*(me^2 - mp^2)/mp, x == -1/2*(me^2 - mp^2)/mp]



On 15 Maj, 01:34, Dox <o.castillo.felis...@gmail.com> wrote:
> Hi again list,
>
> This time I come with a problem of solving an algebraic expression, the
> solution has the variable x on it!
>
> sage: reset()
> sage: var('x')
> sage: var('mp', latex_name=r"m_\pi")
> sage: var('me', latex_name=r"m_e")
> sage: f(x) = mp - sqrt(x^2 + me^2) - x
> sage: solve(f(x)==0, x)
> [x == mp - sqrt(me^2 + x^2)]

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