Trouble with implicit user-defined conversions

Why exactly do I get a compilation error?

You are only allowed one user defined conversion in a conversion sequence. When you do

CoolEnum(CoolEnum::kFirst) == Wrapper<CoolEnum>(CoolEnum(CoolEnum::kFirst)

CoolEnum(CoolEnum::kFirst) can be converted to a CoolEnum::Impl in a single step but Wrapper<CoolEnum>(CoolEnum(CoolEnum::kFirst) first has to convert the Wrapper to a CoolEnum, and then convert that to a CoolEnum::Impl. Since that is two user defined conversions you get an error

What is the best possible fix for CoolEnum class?

Just add a operator == for it. You can then do the comparison of the enum value in there. This will work because it only take a single user defined conversion to go from a Wrapper<T> to T. Changing the code to

#include <cassert>

class CoolEnum {
public:
    enum Impl {
        kFirst, kSecond
    };

    explicit CoolEnum(Impl value) : value_(value) {
    }

    operator Impl() const {
        return value_;
    }

    CoolEnum Inverse() const {
        switch (value_) {
            case kFirst:
                return CoolEnum{kSecond};
            default:
                return CoolEnum{kFirst};
        }
    }
    friend bool operator ==(const CoolEnum& lhs, const CoolEnum& rhs);
    // ^^^^^^^^^^^^^^^^^ added this ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

private:
    Impl value_;
};

bool operator ==(const CoolEnum& lhs, const CoolEnum& rhs)
{
    return lhs.value_ == rhs.value_;
}
// ^^^^^^^^^^^^^^^^^ added this ^^^^^^^^^^^^^^^^^^^^^^^^^^

template <class WrapMe>
class Wrapper {
public:
    Wrapper(WrapMe value, char other_info)
        : value_(value), other_info_(other_info) {
    }

    operator const WrapMe&() const {
        return value_;
    }

private:
    WrapMe value_;
    char other_info_;
};

int main() {
    // compiles
    assert(CoolEnum(CoolEnum::kFirst) == CoolEnum::kFirst);

    // does not compile: no match for operator ==
    assert(CoolEnum(CoolEnum::kFirst)
       == Wrapper<CoolEnum>(CoolEnum(CoolEnum::kFirst), 'e'));
    return 0;
}

lets it compile