How to Solve a System of Absolute Value Equations Algebraically

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How can one find the points of intersections of the two graphs algebraically?

$$f(x) = |(x-1)^2-4|$$

$$f(x) = |x+3|-2$$

I understand that it could be solved graphically and through some sort of system of piecewise functions,

$$f(x) = $$ \begin{cases} (x-1)^2-4, & \text{if $x \le -1$ or $x \ge 3$ } \\ -(x-1)^2+4|, & \text{if $-1\lt x \lt 3$} \end{cases}

$$g(x) = $$ \begin{cases} x+1, & \text{if $x \ge -3$} \\ -x-5, & \text{if $x \lt -3$} \end{cases}

but is there a clean algebraic way to solve it?