Solving a set of quadratic equations

Greetings,

Can some one suggest a method for solving a set of equations of the
form

f_1(x_1) - f_2(x_2) = 0
f_1(x_2) - f_2(x_3) = 0
........................
........................
........................
f_{n-1}(x_{n-1}) - f_n(x_n) = 0
x_1 + x_2 + ... + x_n = N

where f_i(x_i) are second degree polynomials.

thanx

.