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The Coulomb's law of force between two electrically charged particles :
         q
₁ , q₂ = electric charges on the two particles.
           r = distance between two particles = 0.1 m
      the particles are assumed to be point sized.
         Force F = 18 N 

 
      q₁ + q₂ = 9 μ C    --- (1)

Force\ F=\frac{1}{4\pi \epsilon_0}\ \frac{q_1\ q_2}{r^2}\\\\q_1\ q_2=\frac{18*0.1^2}{9*10^9}=20*10^{-12} C,\ \ \ \ --\ (2)

  Solve the two equations to get the values of charges.
     q₁ (9 - q₁) = 20
     q₁² - 9 q₁ + 20 = 0
       (q₁ - 5) (q₁ - 4) = 0

       q₁ = 5 μ C  or  4 μ C
       q₂  = 4 μ C  or  5 μ C


3 5 3