To tackle the optimization problem described, let's first break down the components into a symbolic representation as requested. The variables and their corresponding natural language descriptions are:

- `x0`: hours worked by Paul
- `x1`: hours worked by Dale

The objective function to maximize is: $8.98 \times (x0)^2 + 6.8 \times x0 \times x1$

Given the constraints, we have:
1. Paperwork competence rating for Paul: $3$
2. Organization score for Paul: $4$
3. Paperwork competence rating for Dale: $3$
4. Organization score for Dale: $3$
5. Total combined paperwork competence rating from hours worked by Paul and Dale: $3x0 + 3x1 \geq 4$
6. Total combined organization score from hours worked by Paul squared and hours worked by Dale squared: $4(x0)^2 + 3(x1)^2 \geq 14$
7. Constraint on the combination of squared hours worked: $6(x0)^2 - (x1)^2 \geq 0$
8. Maximum total combined paperwork competence rating from hours worked by Paul squared and hours worked by Dale squared: $3(x0)^2 + 3(x1)^2 \leq 7$
9. Maximum total combined paperwork competence rating from hours worked by Paul and hours worked by Dale: $3x0 + 3x1 \leq 7$
10. Maximum total combined organization score from hours worked by Paul and hours worked by Dale: $4x0 + 3x1 \leq 18$

Let's represent this problem symbolically as requested:

```json
{
    'sym_variables': [('x0', 'hours worked by Paul'), ('x1', 'hours worked by Dale')],
    'objective_function': '8.98 * (x0)**2 + 6.8 * x0 * x1',
    'constraints': [
        '3*x0 >= 3', 
        '4*x0 >= 4', 
        '3*x1 >= 3', 
        '3*x1 >= 3', 
        '3*x0 + 3*x1 >= 4',
        '4*(x0)**2 + 3*(x1)**2 >= 14',
        '6*(x0)**2 - (x1)**2 >= 0',
        '3*(x0)**2 + 3*(x1)**2 <= 7',
        '3*x0 + 3*x1 <= 7',
        '4*x0 + 3*x1 <= 18'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Add variables
x0 = m.addVar(name="hours_worked_by_Paul")
x1 = m.addVar(name="hours_worked_by_Dale")

# Set the objective function
m.setObjective(8.98 * (x0**2) + 6.8 * x0 * x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x0 >= 3)
m.addConstr(4*x0 >= 4)
m.addConstr(3*x1 >= 3)
m.addConstr(3*x1 >= 3)
m.addConstr(3*x0 + 3*x1 >= 4)
m.addConstr(4*(x0**2) + 3*(x1**2) >= 14)
m.addConstr(6*(x0**2) - (x1**2) >= 0)
m.addConstr(3*(x0**2) + 3*(x1**2) <= 7)
m.addConstr(3*x0 + 3*x1 <= 7)
m.addConstr(4*x0 + 3*x1 <= 18)

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Paul: {x0.x}")
    print(f"Hours worked by Dale: {x1.x}")
else:
    print("No optimal solution found")
```