  Asteroid systems such as binaries and pairs are indicative of physical
properties and dynamical histories of the Small Solar System Bodies. Although
numerous observational and theoretical studies have been carried out, the
formation mechanism of asteroid pairs is still unclear, especially for
near-Earth asteroid (NEA) pairs. We conducted a series of optical photometric
and polarimetric observations of a small NEA 2010 XC$_{15}$ in 2022 December to
investigate its surface properties. The rotation period of 2010 XC$_{15}$ is
possibly a few to several dozen hours and color indices of 2010 XC$_{15}$ are
derived as $g-r=0.435\pm0.008$, $r-i=0.158\pm0.017$, and $r-z=0.186\pm0.009$ in
the Pan-STARRS system. The linear polarization degrees of 2010 XC$_{15}$ are a
few percent at the phase angle range of 58$^{\circ}$ to 114$^{\circ}$. We found
that 2010 XC$_{15}$ is a rare E-type NEA on the basis of its photometric and
polarimetric properties. Taking the similarity of not only physical properties
but also dynamical integrals and the rarity of E-type NEAs into account, we
suppose that 2010 XC$_{15}$ and 1998 WT$_{24}$ are of common origin (i.e.,
asteroid pair). These two NEAs are the sixth NEA pair and first E-type NEA pair
ever confirmed, possibly formed by rotational fission. We conjecture that the
parent body of 2010 XC$_{15}$ and 1998 WT$_{24}$ was transported from the
main-belt through the $\nu_6$ resonance or Hungaria region.
