def calc_radii_sep_from_seps(sep_proj_ext, sep_proj_int):
    """Calculate the radii of both binary stars from projections of star separations
    at external and internal tangencies. Method is independent of any inclination assumptions.
    
    Parameters
    ----------
    sep_proj_ext : float
        Projected separation of star centers at external tangencies.
        (e.g. begin ingress, end egress). Unit is star-star separation distance.
    sep_proj_int : float
        Projected separation of star centers at internal tangencies.
        (e.g. end ingress, begin egress). Unit is star-star separation distance.
    
    Returns
    -------
    radius_sep_s : float
        Radius of smaller-sized star. Unit is star-star separation distance.
    radius_sep_g : float
        Radius of greater-sized star. Unit is star-star separation distance.
    
    See Also
    --------
    calc_radii_ratio_from_light, calc_radius_from_velrs_times 
    
    Notes
    -----
    Note: Radii are returned as a tuple: (rs, rg)
    Note: Method does not assume an inclination.
    radii_ratio = radius_sep_s / radius_sep_g
    sep_proj_ext = radius_sep_g * (1 + radii_ratio)
    sep_proj_int = radius_sep_g * (1 - radii_ratio)
    => sep_proj_ext - sep_proj_int = 2 * radius_sep_g * radii_ratio = 2 * radius_sep_s
       radius_sep_s = (sep_proj_ext - sep_proj_int) / 2
    => sep_proj_ext + sep_proj_int = 2 * radius_sep_g
       radius_sep_g = (sep_proj_ext + sep_proj_int) / 2
    From equations 7.8, 7.9, 7.10 in section 7.3 of [1]_.
    
    References
    ----------
    .. [1] Budding, 2007, Introduction to Astronomical Photometry
    
    """
    radius_sep_s = (sep_proj_ext - sep_proj_int) / 2.0
    radius_sep_g = (sep_proj_ext + sep_proj_int) / 2.0
    return radius_sep_s, radius_sep_g
