How to solve a system of complex equations with assumptions?

[moorepants]

I have these two equations:

     ____________________   _______   _______                     
20⋅╲╱ -(-l + t)⋅(-l + w) ⋅╲╱ l + t ⋅╲╱ l + w                      
───────────────────────────────────────────── = 15.9458629325234⋅ⅈ
             _________    _________                               
            ╱  2    2    ╱  2    2                                
          ╲╱  l  + t  ⋅╲╱  l  + w                                 

     ___________________   _______   _______                    
20⋅╲╱ -(-l + t)⋅(t - w) ⋅╲╱ l + t ⋅╲╱ t + w                     
──────────────────────────────────────────── = 19.651765960555⋅ⅈ
            _________    _________                              
           ╱  2    2    ╱  2    2                               
         ╲╱  l  + t  ⋅╲╱  t  + w                                

I'd like to solve them for w and t given l > w > t > 0. I'm guessing I have to use the new assumptions system + solve() or nonlinsolve(). How might I do that? It isn't too clear if that is possible.

[moorepants]

Maybe substituting t - l and w-l with a positive symbol could deal with the inequality assumption.

[oscarbenjamin]

Can you show the repr of the equations (or simple code to make them)?

You could unrad the equations and filter the resulting solutions.

[moorepants]

Equality(Mul(Integer(20), Pow(Mul(Integer(-1), Add(Mul(Integer(-1), Symbol('l', positive=True)), Symbol('t', positive=True)), Add(Mul(Integer(-1), Symbol('l', positive=True)), Symbol('w', positive=True))), Rational(1, 2)), Pow(Add(Symbol('l', positive=True), Symbol('t', positive=True)), Rational(1, 2)), Pow(Add(Symbol('l', positive=True), Symbol('w', positive=True)), Rational(1, 2)), Pow(Add(Pow(Symbol('l', positive=True), Integer(2)), Pow(Symbol('t', positive=True), Integer(2))), Rational(-1, 2)), Pow(Add(Pow(Symbol('l', positive=True), Integer(2)), Pow(Symbol('w', positive=True), Integer(2))), Rational(-1, 2))), Mul(Float('15.945862932523401', precision=53), I))

Equality(Mul(Integer(20), Pow(Mul(Integer(-1), Add(Mul(Integer(-1), Symbol('l', positive=True)), Symbol('t', positive=True)), Add(Symbol('t', positive=True), Mul(Integer(-1), Symbol('w', positive=True)))), Rational(1, 2)), Pow(Add(Symbol('l', positive=True), Symbol('t', positive=True)), Rational(1, 2)), Pow(Add(Pow(Symbol('l', positive=True), Integer(2)), Pow(Symbol('t', positive=True), Integer(2))), Rational(-1, 2)), Pow(Add(Symbol('t', positive=True), Symbol('w', positive=True)), Rational(1, 2)), Pow(Add(Pow(Symbol('t', positive=True), Integer(2)), Pow(Symbol('w', positive=True), Integer(2))), Rational(-1, 2))), Mul(Float('19.651765960555', precision=53), I))

[moorepants]

You could unrad the equations and filter the resulting solutions.

I tried that but didn't get where I wanted. Can try again.

[moorepants]

Actually, unrad with solve() did give about what I want.