And if yes, then how can it be resolved?
As far as I know in standard set theory it's true that "no set is its own member". Also in standard logic the law of excluded middle is true, either $A$ or $\lnot A$.
Now let's consider simple sentence "Entity $X$ is either a real number or not a real number". This can be restated in terms of set theory as "Element $x$ either belongs to set $\mathbb{R}$ or to set non-$\mathbb{R}$".
Looks like a tautology, doesn't it? But I will show you that it's not because there is one thing that isn't a member of either set. Namely, it's set "non-$\mathbb{R}$". This can't belong to set $\mathbb{R}$ because it isn't a real number. This also can't belong to set non-$\mathbb{R}$ (i.e. it can't belong to itself) because of "no set is its own member". Thus "Element $x$ either belongs to set $\mathbb{R}$ or to set non-$\mathbb{R}$" isn't a tautology.