If you place a point charge at the point you wish to know the E-field, the E-field is not well defined here. The E-field magnitude becomes arbitrarily large as you approach this point.
If on the other hand you have an extended spherical charged sphere placed at the point you are measuring the E-field, the answer depends. If the free charge distribution in this sphere is spherically symmetric and the sphere is a non-polarizable insulator (its permittivity is $\epsilon_0$), then the value of the E-field is not affected by this sphere. This is because the E-field here is the superposition of the E-field due to the charged sphere and the positive charge on the right, and because of the spherical symmetry, the E-field due to the sphere at the center of this sphere is zero.
In other cases, if you still assume extended charges, but the charge distribution is no longer spherically symmetric or the charged object is made of a dielectric with $\epsilon \ne \epsilon_0$, the E-field will in general be different from the case with only the positive charge.