It looks like you've shared an image with two equations. Let me interpret them and provide solutions or analysis for both:

1. Equation (E1): $3 - 2e^{x^2 - 1} = 0 \quad \text{on} \, \mathbb{R}$

   To solve this equation, we'll first isolate the exponential term and then simplify the equation.

2. Equation (E2): $\ln(1 + e^{-x}) = 3 \quad \text{on} \, \mathbb{R}$

   Similarly, we'll isolate the logarithmic term to find the solution.

Let me know if you want to dive into the steps of solving these equations!