logistic regression coefs to excel formulation
By running a logistic regression model, the objective is to get the chance of a binary outcome based on the different predictor variables. Since the result is a chance, what is modeled is actually:

$$
log \left(\frac{P_{+}}{1 - P_{+}}\right) = \beta_{0} + \beta_{1}x_{1} + ... + \beta_{n}x_{n}
$$

So the coefficients you get from R are the $\beta$ values.
The function you have so far in Excel computes correctly the right hand side (RHS) of the above equation, but to get the probability $P_{+}$, you need to solve the equation for it. Let's call the RHS, $\mathbf{Bx}$

$$
log \left(\frac{P_{+}}{1 - P_{+}}\right) = \mathbf{Bx} \\
\frac{P_{+}}{1 - P_{+}} = e^{\mathbf{Bx}} \\
\frac{1}{e^{\mathbf{Bx}}} = \frac{1}{P_{+}} - 1 \\
\frac{e^{\mathbf{Bx}} + 1}{e^{\mathbf{Bx}}} = \frac{1}{P_{+}} \\
P_{+} = \frac{1}{1 + e^{-\mathbf{Bx}}}
$$

To your results, apply this transformation and you should get the same results as the predict function in R.