= Solution
In the <pion> <rest frame>, conservation of three-momentum makes the <Electron> and massless <neutrino> momenta equal and opposite, of common magnitude $p$. Their energies obey
$$
E_e+pc=m_\pi c^2,\qquad E_e^2=p^2c^2+m_e^2c^4.
$$
Squaring $E_e=m_\pi c^2-pc$ and cancelling $p^2c^2$ gives
$$
pc=\frac{m_\pi^2-m_e^2}{2m_\pi}c^2,\qquad E_e=\frac{m_\pi^2+m_e^2}{2m_\pi}c^2.
$$
The <Electron> <four-momentum> satisfies $p=E_ev/c^2$. Thus, for the physically allowed decay $m_\pi>m_e$,
$$
\boxed{v=c\frac{m_\pi^2-m_e^2}{m_\pi^2+m_e^2}=c\frac{1-(m_e/m_\pi)^2}{1+(m_e/m_\pi)^2}.}
$$
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